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

Percentage Accurate: 97.6% → 95.9%

Time: 7.3s

Alternatives: 12

Speedup: 1.0×

• 24.1% 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: 97.6% 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: 95.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000000000:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -500000000000.0)
   (/ (- y x) (/ t z))
   (if (<= (/ z t) 10.0) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -500000000000.0) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 10.0) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-500000000000.0d0)) then
        tmp = (y - x) / (t / z)
    else if ((z / t) <= 10.0d0) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -500000000000.0) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 10.0) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -500000000000.0:
		tmp = (y - x) / (t / z)
	elif (z / t) <= 10.0:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -500000000000.0)
		tmp = Float64(Float64(y - x) / Float64(t / z));
	elseif (Float64(z / t) <= 10.0)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -500000000000.0)
		tmp = (y - x) / (t / z);
	elseif ((z / t) <= 10.0)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -500000000000.0], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 10.0], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 94.2%

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

      1. *-commutative 94.2%

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

      2. sub-div 95.6%

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

      3. associate-/r/ 97.4%

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

      4. frac-2neg 97.4%

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

      5. frac-2neg 97.4%

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

      6. sub-neg 97.4%

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

      7. distribute-neg-in 97.4%

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

      8. add-sqr-sqrt 52.7%

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

      9. sqrt-unprod 69.0%

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

      10. sqr-neg 69.0%

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

      11. sqrt-unprod 18.7%

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

      12. add-sqr-sqrt 50.1%

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

      13. add-sqr-sqrt 31.4%

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

      14. sqrt-unprod 69.4%

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

      15. sqr-neg 69.4%

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

      16. sqrt-unprod 44.6%

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

      17. add-sqr-sqrt 97.4%

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

      18. distribute-neg-frac 97.4%

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

   4. Applied egg-rr 97.4%

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

      1. distribute-neg-in 97.4%

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

      2. remove-double-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. distribute-neg-frac 97.4%

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

      5. remove-double-neg 97.4%

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

   6. Simplified 97.4%

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

   if -5e11 < (/.f64 z t) < 10

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 93.2%

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

      1. associate-*r/ 97.8%

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

   4. Simplified 97.8%

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

   if 10 < (/.f64 z t)

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 95.2%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. mul-1-neg 95.2%

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

      3. sub-neg 95.2%

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

      4. div-sub 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000000000:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 2: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ t_2 := \frac{z}{t} \cdot \left(-x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -0.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)) (t_2 (* (/ z t) (- x))))
   (if (<= (/ z t) -2e+176)
     (* y (/ z t))
     (if (<= (/ z t) -5e+116)
       t_2
       (if (<= (/ z t) -4e+51)
         t_1
         (if (<= (/ z t) -0.5)
           t_2
           (if (<= (/ z t) 5e-87)
             x
             (if (<= (/ z t) 4e+150)
               (/ y (/ t z))
               (if (<= (/ z t) 1e+184) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double t_2 = (z / t) * -x;
	double tmp;
	if ((z / t) <= -2e+176) {
		tmp = y * (z / t);
	} else if ((z / t) <= -5e+116) {
		tmp = t_2;
	} else if ((z / t) <= -4e+51) {
		tmp = t_1;
	} else if ((z / t) <= -0.5) {
		tmp = t_2;
	} else if ((z / t) <= 5e-87) {
		tmp = x;
	} else if ((z / t) <= 4e+150) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e+184) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / t
    t_2 = (z / t) * -x
    if ((z / t) <= (-2d+176)) then
        tmp = y * (z / t)
    else if ((z / t) <= (-5d+116)) then
        tmp = t_2
    else if ((z / t) <= (-4d+51)) then
        tmp = t_1
    else if ((z / t) <= (-0.5d0)) then
        tmp = t_2
    else if ((z / t) <= 5d-87) then
        tmp = x
    else if ((z / t) <= 4d+150) then
        tmp = y / (t / z)
    else if ((z / t) <= 1d+184) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double t_2 = (z / t) * -x;
	double tmp;
	if ((z / t) <= -2e+176) {
		tmp = y * (z / t);
	} else if ((z / t) <= -5e+116) {
		tmp = t_2;
	} else if ((z / t) <= -4e+51) {
		tmp = t_1;
	} else if ((z / t) <= -0.5) {
		tmp = t_2;
	} else if ((z / t) <= 5e-87) {
		tmp = x;
	} else if ((z / t) <= 4e+150) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e+184) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / t
	t_2 = (z / t) * -x
	tmp = 0
	if (z / t) <= -2e+176:
		tmp = y * (z / t)
	elif (z / t) <= -5e+116:
		tmp = t_2
	elif (z / t) <= -4e+51:
		tmp = t_1
	elif (z / t) <= -0.5:
		tmp = t_2
	elif (z / t) <= 5e-87:
		tmp = x
	elif (z / t) <= 4e+150:
		tmp = y / (t / z)
	elif (z / t) <= 1e+184:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / t)
	t_2 = Float64(Float64(z / t) * Float64(-x))
	tmp = 0.0
	if (Float64(z / t) <= -2e+176)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= -5e+116)
		tmp = t_2;
	elseif (Float64(z / t) <= -4e+51)
		tmp = t_1;
	elseif (Float64(z / t) <= -0.5)
		tmp = t_2;
	elseif (Float64(z / t) <= 5e-87)
		tmp = x;
	elseif (Float64(z / t) <= 4e+150)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 1e+184)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / t;
	t_2 = (z / t) * -x;
	tmp = 0.0;
	if ((z / t) <= -2e+176)
		tmp = y * (z / t);
	elseif ((z / t) <= -5e+116)
		tmp = t_2;
	elseif ((z / t) <= -4e+51)
		tmp = t_1;
	elseif ((z / t) <= -0.5)
		tmp = t_2;
	elseif ((z / t) <= 5e-87)
		tmp = x;
	elseif ((z / t) <= 4e+150)
		tmp = y / (t / z);
	elseif ((z / t) <= 1e+184)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+176], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+116], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], -4e+51], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -0.5], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 5e-87], x, If[LessEqual[N[(z / t), $MachinePrecision], 4e+150], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+184], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -2e176

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 97.3%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. associate-*r/ 67.8%

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

      2. associate-*l/ 79.4%

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

      3. *-commutative 79.4%

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

      4. clear-num 79.4%

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

      5. un-div-inv 79.3%

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

   5. Applied egg-rr 79.3%

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

      1. *-un-lft-identity 79.3%

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

      2. associate-*l/ 79.4%

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

      3. clear-num 79.4%

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

   7. Applied egg-rr 79.4%

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

   if -2e176 < (/.f64 z t) < -5.00000000000000025e116 or -4e51 < (/.f64 z t) < -0.5 or 3.99999999999999992e150 < (/.f64 z t) < 1.00000000000000002e184

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 96.1%

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

   3. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. mul-1-neg 75.5%

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

   5. Simplified 75.5%

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

      1. *-commutative 75.5%

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

      2. distribute-frac-neg 75.5%

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

      3. distribute-lft-neg-out 75.5%

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

      4. add-sqr-sqrt 42.1%

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

      5. sqrt-unprod 34.9%

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

      6. sqr-neg 34.9%

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

      7. sqrt-unprod 0.5%

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

      8. add-sqr-sqrt 0.9%

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

      9. div-inv 0.9%

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

      10. associate-*l* 1.0%

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

      11. associate-/r/ 1.0%

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

      12. clear-num 1.0%

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

      13. add-sqr-sqrt 0.5%

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

      14. sqrt-unprod 35.0%

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

      15. sqr-neg 35.0%

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

      16. sqrt-unprod 42.1%

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

      17. add-sqr-sqrt 75.8%

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

   7. Applied egg-rr 75.8%

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

   if -5.00000000000000025e116 < (/.f64 z t) < -4e51 or 1.00000000000000002e184 < (/.f64 z t)

   1. Initial program 93.3%

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

   2. Taylor expanded in z around inf 91.0%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. associate-*r/ 65.3%

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

   5. Applied egg-rr 65.3%

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

   if -0.5 < (/.f64 z t) < 5.00000000000000042e-87

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 73.9%

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

   if 5.00000000000000042e-87 < (/.f64 z t) < 3.99999999999999992e150

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 72.5%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. associate-*r/ 60.5%

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

      2. associate-*l/ 71.0%

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

      3. *-commutative 71.0%

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

      4. clear-num 70.9%

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

      5. un-div-inv 71.1%

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

   5. Applied egg-rr 71.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+51}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -0.5:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+184}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]

Alternative 3: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -0.5:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+184}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+176)
   (* y (/ z t))
   (if (<= (/ z t) -0.5)
     (* z (/ (- x) t))
     (if (<= (/ z t) 5e-87)
       x
       (if (<= (/ z t) 4e+150)
         (/ y (/ t z))
         (if (<= (/ z t) 1e+184) (* (/ z t) (- x)) (/ (* y z) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+176) {
		tmp = y * (z / t);
	} else if ((z / t) <= -0.5) {
		tmp = z * (-x / t);
	} else if ((z / t) <= 5e-87) {
		tmp = x;
	} else if ((z / t) <= 4e+150) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e+184) {
		tmp = (z / t) * -x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d+176)) then
        tmp = y * (z / t)
    else if ((z / t) <= (-0.5d0)) then
        tmp = z * (-x / t)
    else if ((z / t) <= 5d-87) then
        tmp = x
    else if ((z / t) <= 4d+150) then
        tmp = y / (t / z)
    else if ((z / t) <= 1d+184) then
        tmp = (z / t) * -x
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+176) {
		tmp = y * (z / t);
	} else if ((z / t) <= -0.5) {
		tmp = z * (-x / t);
	} else if ((z / t) <= 5e-87) {
		tmp = x;
	} else if ((z / t) <= 4e+150) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e+184) {
		tmp = (z / t) * -x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+176:
		tmp = y * (z / t)
	elif (z / t) <= -0.5:
		tmp = z * (-x / t)
	elif (z / t) <= 5e-87:
		tmp = x
	elif (z / t) <= 4e+150:
		tmp = y / (t / z)
	elif (z / t) <= 1e+184:
		tmp = (z / t) * -x
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+176)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= -0.5)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (Float64(z / t) <= 5e-87)
		tmp = x;
	elseif (Float64(z / t) <= 4e+150)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 1e+184)
		tmp = Float64(Float64(z / t) * Float64(-x));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e+176)
		tmp = y * (z / t);
	elseif ((z / t) <= -0.5)
		tmp = z * (-x / t);
	elseif ((z / t) <= 5e-87)
		tmp = x;
	elseif ((z / t) <= 4e+150)
		tmp = y / (t / z);
	elseif ((z / t) <= 1e+184)
		tmp = (z / t) * -x;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+176], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -0.5], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-87], x, If[LessEqual[N[(z / t), $MachinePrecision], 4e+150], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+184], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 z t) < -2e176

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 97.3%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. associate-*r/ 67.8%

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

      2. associate-*l/ 79.4%

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

      3. *-commutative 79.4%

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

      4. clear-num 79.4%

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

      5. un-div-inv 79.3%

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

   5. Applied egg-rr 79.3%

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

      1. *-un-lft-identity 79.3%

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

      2. associate-*l/ 79.4%

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

      3. clear-num 79.4%

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

   7. Applied egg-rr 79.4%

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

   if -2e176 < (/.f64 z t) < -0.5

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 91.6%

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

   3. Taylor expanded in y around 0 65.7%

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

      1. associate-*r/ 65.7%

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

      2. mul-1-neg 65.7%

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

   5. Simplified 65.7%

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

   if -0.5 < (/.f64 z t) < 5.00000000000000042e-87

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 73.9%

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

   if 5.00000000000000042e-87 < (/.f64 z t) < 3.99999999999999992e150

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 72.5%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. associate-*r/ 60.5%

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

      2. associate-*l/ 71.0%

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

      3. *-commutative 71.0%

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

      4. clear-num 70.9%

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

      5. un-div-inv 71.1%

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

   5. Applied egg-rr 71.1%

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

   if 3.99999999999999992e150 < (/.f64 z t) < 1.00000000000000002e184

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.5%

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

   3. Taylor expanded in y around 0 73.3%

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

      1. associate-*r/ 73.3%

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

      2. mul-1-neg 73.3%

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

   5. Simplified 73.3%

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

      1. *-commutative 73.3%

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

      2. distribute-frac-neg 73.3%

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

      3. distribute-lft-neg-out 73.3%

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

      4. add-sqr-sqrt 44.4%

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

      5. sqrt-unprod 45.1%

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

      6. sqr-neg 45.1%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 0.8%

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

      9. div-inv 0.8%

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

      10. associate-*l* 0.8%

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

      11. associate-/r/ 0.8%

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

      12. clear-num 0.8%

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

      13. add-sqr-sqrt 0.7%

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

      14. sqrt-unprod 45.3%

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

      15. sqr-neg 45.3%

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

      16. sqrt-unprod 44.4%

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

      17. add-sqr-sqrt 73.8%

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

   7. Applied egg-rr 73.8%

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

   if 1.00000000000000002e184 < (/.f64 z t)

   1. Initial program 91.0%

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

   2. Taylor expanded in z around inf 93.6%

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

   3. Taylor expanded in y around inf 61.4%

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

      1. associate-*r/ 61.5%

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

   5. Applied egg-rr 61.5%

      \[\leadsto \color{blue}{\frac{z \cdot y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -0.5:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+184}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]

Alternative 4: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= (/ z t) -5e-14)
     t_1
     (if (<= (/ z t) 5e-87)
       (* x (- 1.0 (/ z t)))
       (if (<= (/ z t) 5e-43) (* y (/ z t)) (if (<= (/ z t) 2e-29) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -5e-14) {
		tmp = t_1;
	} else if ((z / t) <= 5e-87) {
		tmp = x * (1.0 - (z / t));
	} else if ((z / t) <= 5e-43) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / t)
    if ((z / t) <= (-5d-14)) then
        tmp = t_1
    else if ((z / t) <= 5d-87) then
        tmp = x * (1.0d0 - (z / t))
    else if ((z / t) <= 5d-43) then
        tmp = y * (z / t)
    else if ((z / t) <= 2d-29) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -5e-14) {
		tmp = t_1;
	} else if ((z / t) <= 5e-87) {
		tmp = x * (1.0 - (z / t));
	} else if ((z / t) <= 5e-43) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-29) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if (z / t) <= -5e-14:
		tmp = t_1
	elif (z / t) <= 5e-87:
		tmp = x * (1.0 - (z / t))
	elif (z / t) <= 5e-43:
		tmp = y * (z / t)
	elif (z / t) <= 2e-29:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e-14)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-87)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	elseif (Float64(z / t) <= 5e-43)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 2e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if ((z / t) <= -5e-14)
		tmp = t_1;
	elseif ((z / t) <= 5e-87)
		tmp = x * (1.0 - (z / t));
	elseif ((z / t) <= 5e-43)
		tmp = y * (z / t);
	elseif ((z / t) <= 2e-29)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e-14], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-87], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-43], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-29], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -5.0000000000000002e-14 or 1.99999999999999989e-29 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 91.8%

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

   3. Taylor expanded in y around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. mul-1-neg 91.8%

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

      3. sub-neg 91.8%

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

      4. div-sub 93.9%

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

   5. Simplified 93.9%

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

   if -5.0000000000000002e-14 < (/.f64 z t) < 5.00000000000000042e-87

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

   4. Simplified 76.4%

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

   if 5.00000000000000042e-87 < (/.f64 z t) < 5.00000000000000019e-43

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 62.0%

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

   3. Taylor expanded in y around inf 62.7%

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

      1. associate-*r/ 63.1%

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

      2. associate-*l/ 83.5%

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

      3. *-commutative 83.5%

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

      4. clear-num 83.5%

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

      5. un-div-inv 83.5%

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

   5. Applied egg-rr 83.5%

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

      1. *-un-lft-identity 83.5%

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

      2. associate-*l/ 83.5%

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

      3. clear-num 83.5%

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

   7. Applied egg-rr 83.5%

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

   if 5.00000000000000019e-43 < (/.f64 z t) < 1.99999999999999989e-29

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 5: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-26} \lor \neg \left(x \leq 1.04 \cdot 10^{-103} \lor \neg \left(x \leq 1.2 \cdot 10^{-8}\right) \land x \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.2e-26)
         (not (or (<= x 1.04e-103) (and (not (<= x 1.2e-8)) (<= x 4e+28)))))
   (* x (- 1.0 (/ z t)))
   (/ y (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e-26) || !((x <= 1.04e-103) || (!(x <= 1.2e-8) && (x <= 4e+28)))) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = 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 ((x <= (-8.2d-26)) .or. (.not. (x <= 1.04d-103) .or. (.not. (x <= 1.2d-8)) .and. (x <= 4d+28))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = 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 ((x <= -8.2e-26) || !((x <= 1.04e-103) || (!(x <= 1.2e-8) && (x <= 4e+28)))) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.2e-26) or not ((x <= 1.04e-103) or (not (x <= 1.2e-8) and (x <= 4e+28))):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.2e-26) || !((x <= 1.04e-103) || (!(x <= 1.2e-8) && (x <= 4e+28))))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.2e-26) || ~(((x <= 1.04e-103) || (~((x <= 1.2e-8)) && (x <= 4e+28)))))
		tmp = x * (1.0 - (z / t));
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.2e-26], N[Not[Or[LessEqual[x, 1.04e-103], And[N[Not[LessEqual[x, 1.2e-8]], $MachinePrecision], LessEqual[x, 4e+28]]]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999997e-26 or 1.04000000000000001e-103 < x < 1.19999999999999999e-8 or 3.99999999999999983e28 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   4. Simplified 87.3%

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

   if -8.1999999999999997e-26 < x < 1.04000000000000001e-103 or 1.19999999999999999e-8 < x < 3.99999999999999983e28

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 75.9%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. associate-*r/ 68.8%

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

      2. associate-*l/ 75.3%

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

      3. *-commutative 75.3%

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

      4. clear-num 75.3%

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

      5. un-div-inv 75.5%

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

   5. Applied egg-rr 75.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-26} \lor \neg \left(x \leq 1.04 \cdot 10^{-103} \lor \neg \left(x \leq 1.2 \cdot 10^{-8}\right) \land x \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000000000 \lor \neg \left(\frac{z}{t} \leq 10\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -500000000000.0) (not (<= (/ z t) 10.0)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500000000000.0) || !((z / t) <= 10.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-500000000000.0d0)) .or. (.not. ((z / t) <= 10.0d0))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500000000000.0) || !((z / t) <= 10.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -500000000000.0) or not ((z / t) <= 10.0):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -500000000000.0) || !(Float64(z / t) <= 10.0))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -500000000000.0) || ~(((z / t) <= 10.0)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -500000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 10.0]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5e11 or 10 < (/.f64 z t)

   1. Initial program 96.3%

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

   2. Taylor expanded in z around inf 94.6%

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

   3. Taylor expanded in y around 0 94.6%

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

      1. +-commutative 94.6%

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

      2. mul-1-neg 94.6%

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

      3. sub-neg 94.6%

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

      4. div-sub 96.9%

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

   5. Simplified 96.9%

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

   if -5e11 < (/.f64 z t) < 10

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 93.2%

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

      1. associate-*r/ 97.8%

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

   4. Simplified 97.8%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000000000 \lor \neg \left(\frac{z}{t} \leq 10\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-14} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-87}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-14) (not (<= (/ z t) 5e-87))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-14) || !((z / t) <= 5e-87)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d-14)) .or. (.not. ((z / t) <= 5d-87))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-14) || !((z / t) <= 5e-87)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-14) or not ((z / t) <= 5e-87):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-14) || !(Float64(z / t) <= 5e-87))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e-14) || ~(((z / t) <= 5e-87)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-14], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-87]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.0000000000000002e-14 or 5.00000000000000042e-87 < (/.f64 z t)

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 87.8%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. associate-*r/ 53.9%

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

      2. associate-*l/ 60.5%

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

      3. *-commutative 60.5%

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

      4. clear-num 60.5%

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

      5. un-div-inv 60.6%

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

   5. Applied egg-rr 60.6%

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

      1. *-un-lft-identity 60.6%

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

      2. associate-*l/ 60.5%

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

      3. clear-num 60.5%

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

   7. Applied egg-rr 60.5%

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

   if -5.0000000000000002e-14 < (/.f64 z t) < 5.00000000000000042e-87

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 76.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-14} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-87}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-14} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-14) (not (<= (/ z t) 5e-87))) (/ y (/ t z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-14) || !((z / t) <= 5e-87)) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d-14)) .or. (.not. ((z / t) <= 5d-87))) then
        tmp = y / (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-14) || !((z / t) <= 5e-87)) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-14) or not ((z / t) <= 5e-87):
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-14) || !(Float64(z / t) <= 5e-87))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e-14) || ~(((z / t) <= 5e-87)))
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-14], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-87]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.0000000000000002e-14 or 5.00000000000000042e-87 < (/.f64 z t)

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 87.8%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. associate-*r/ 53.9%

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

      2. associate-*l/ 60.5%

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

      3. *-commutative 60.5%

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

      4. clear-num 60.5%

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

      5. un-div-inv 60.6%

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

   5. Applied egg-rr 60.6%

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

   if -5.0000000000000002e-14 < (/.f64 z t) < 5.00000000000000042e-87

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 76.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-14} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-155} \lor \neg \left(z \leq 2.22 \cdot 10^{+30}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-155) (not (<= z 2.22e+30))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-155) || !(z <= 2.22e+30)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.7d-155)) .or. (.not. (z <= 2.22d+30))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-155) || !(z <= 2.22e+30)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-155) or not (z <= 2.22e+30):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-155) || !(z <= 2.22e+30))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-155) || ~((z <= 2.22e+30)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-155], N[Not[LessEqual[z, 2.22e+30]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-155 or 2.22e30 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 81.5%

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

   3. Taylor expanded in y around inf 53.3%

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

   if -1.7e-155 < z < 2.22e30

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 62.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-155} \lor \neg \left(z \leq 2.22 \cdot 10^{+30}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 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 97.5%

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

2. Taylor expanded in y around 0 87.7%

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

   1. +-commutative 87.7%

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

   2. mul-1-neg 87.7%

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

   3. sub-neg 87.7%

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

   4. associate-/l* 88.9%

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

   5. associate-/l* 91.8%

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

   6. div-sub 97.7%

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

4. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

2. Final simplification 97.5%

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

Alternative 12: 39.3% 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 97.5%

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

2. Taylor expanded in z around 0 33.9%

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

3. Final simplification 33.9%

   \[\leadsto x \]

Developer target: 97.4% 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 2023308 
(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))))