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

Percentage Accurate: 97.4% → 97.5%

Time: 7.5s

Alternatives: 12

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% 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 97.2%

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

   2. un-div-inv 97.5%

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

4. Applied egg-rr 97.5%

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

5. Final simplification 97.5%

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

Alternative 2: 64.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+69} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+208}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))))
   (if (<= (/ z t) (- INFINITY))
     t_1
     (if (<= (/ z t) -2e+191)
       (* z (/ y t))
       (if (<= (/ z t) -2.0)
         t_1
         (if (<= (/ z t) 5e-17)
           x
           (if (<= (/ z t) 5e+31)
             (* y (/ z t))
             (if (or (<= (/ z t) 4e+69) (not (<= (/ z t) 2e+208)))
               t_1
               (/ (* y z) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if ((z / t) <= -((double) INFINITY)) {
		tmp = t_1;
	} else if ((z / t) <= -2e+191) {
		tmp = z * (y / t);
	} else if ((z / t) <= -2.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e-17) {
		tmp = x;
	} else if ((z / t) <= 5e+31) {
		tmp = y * (z / t);
	} else if (((z / t) <= 4e+69) || !((z / t) <= 2e+208)) {
		tmp = t_1;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if ((z / t) <= -2e+191) {
		tmp = z * (y / t);
	} else if ((z / t) <= -2.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e-17) {
		tmp = x;
	} else if ((z / t) <= 5e+31) {
		tmp = y * (z / t);
	} else if (((z / t) <= 4e+69) || !((z / t) <= 2e+208)) {
		tmp = t_1;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = t_1
	elif (z / t) <= -2e+191:
		tmp = z * (y / t)
	elif (z / t) <= -2.0:
		tmp = t_1
	elif (z / t) <= 5e-17:
		tmp = x
	elif (z / t) <= 5e+31:
		tmp = y * (z / t)
	elif ((z / t) <= 4e+69) or not ((z / t) <= 2e+208):
		tmp = t_1
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = t_1;
	elseif (Float64(z / t) <= -2e+191)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= -2.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-17)
		tmp = x;
	elseif (Float64(z / t) <= 5e+31)
		tmp = Float64(y * Float64(z / t));
	elseif ((Float64(z / t) <= 4e+69) || !(Float64(z / t) <= 2e+208))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = t_1;
	elseif ((z / t) <= -2e+191)
		tmp = z * (y / t);
	elseif ((z / t) <= -2.0)
		tmp = t_1;
	elseif ((z / t) <= 5e-17)
		tmp = x;
	elseif ((z / t) <= 5e+31)
		tmp = y * (z / t);
	elseif (((z / t) <= 4e+69) || ~(((z / t) <= 2e+208)))
		tmp = t_1;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], (-Infinity)], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -2e+191], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-17], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+31], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z / t), $MachinePrecision], 4e+69], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e+208]], $MachinePrecision]], t$95$1, N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -inf.0 or -2.00000000000000015e191 < (/.f64 z t) < -2 or 5.00000000000000027e31 < (/.f64 z t) < 4.0000000000000003e69 or 2e208 < (/.f64 z t)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in z around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-frac-neg2 74.0%

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

   8. Simplified 74.0%

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

   if -inf.0 < (/.f64 z t) < -2.00000000000000015e191

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 69.6%

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

   if -2 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 75.7%

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

   if 4.9999999999999999e-17 < (/.f64 z t) < 5.00000000000000027e31

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate--l+ 87.6%

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

      2. div-sub 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in x around 0 63.8%

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

      1. *-commutative 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in z around 0 63.8%

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

       1. associate-*r/ 87.3%

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

       2. *-commutative 87.3%

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

   11. Simplified 87.3%

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

   if 4.0000000000000003e69 < (/.f64 z t) < 2e208

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in x around 0 84.7%

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

      1. *-commutative 84.7%

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

   8. Simplified 84.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+69} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+208}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+69} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+208}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))))
   (if (<= (/ z t) (- INFINITY))
     (* z (/ x (- t)))
     (if (<= (/ z t) -2e+191)
       (* z (/ y t))
       (if (<= (/ z t) -2.0)
         t_1
         (if (<= (/ z t) 5e-17)
           x
           (if (<= (/ z t) 5e+31)
             (* y (/ z t))
             (if (or (<= (/ z t) 4e+69) (not (<= (/ z t) 2e+208)))
               t_1
               (/ (* y z) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if ((z / t) <= -((double) INFINITY)) {
		tmp = z * (x / -t);
	} else if ((z / t) <= -2e+191) {
		tmp = z * (y / t);
	} else if ((z / t) <= -2.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e-17) {
		tmp = x;
	} else if ((z / t) <= 5e+31) {
		tmp = y * (z / t);
	} else if (((z / t) <= 4e+69) || !((z / t) <= 2e+208)) {
		tmp = t_1;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (x / -t);
	} else if ((z / t) <= -2e+191) {
		tmp = z * (y / t);
	} else if ((z / t) <= -2.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e-17) {
		tmp = x;
	} else if ((z / t) <= 5e+31) {
		tmp = y * (z / t);
	} else if (((z / t) <= 4e+69) || !((z / t) <= 2e+208)) {
		tmp = t_1;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = z * (x / -t)
	elif (z / t) <= -2e+191:
		tmp = z * (y / t)
	elif (z / t) <= -2.0:
		tmp = t_1
	elif (z / t) <= 5e-17:
		tmp = x
	elif (z / t) <= 5e+31:
		tmp = y * (z / t)
	elif ((z / t) <= 4e+69) or not ((z / t) <= 2e+208):
		tmp = t_1
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (Float64(z / t) <= -2e+191)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= -2.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-17)
		tmp = x;
	elseif (Float64(z / t) <= 5e+31)
		tmp = Float64(y * Float64(z / t));
	elseif ((Float64(z / t) <= 4e+69) || !(Float64(z / t) <= 2e+208))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = z * (x / -t);
	elseif ((z / t) <= -2e+191)
		tmp = z * (y / t);
	elseif ((z / t) <= -2.0)
		tmp = t_1;
	elseif ((z / t) <= 5e-17)
		tmp = x;
	elseif ((z / t) <= 5e+31)
		tmp = y * (z / t);
	elseif (((z / t) <= 4e+69) || ~(((z / t) <= 2e+208)))
		tmp = t_1;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], (-Infinity)], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2e+191], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-17], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+31], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z / t), $MachinePrecision], 4e+69], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e+208]], $MachinePrecision]], t$95$1, N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 86.7%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-frac-neg2 87.3%

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

   6. Simplified 87.3%

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

   if -inf.0 < (/.f64 z t) < -2.00000000000000015e191

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 69.6%

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

   if -2.00000000000000015e191 < (/.f64 z t) < -2 or 5.00000000000000027e31 < (/.f64 z t) < 4.0000000000000003e69 or 2e208 < (/.f64 z t)

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. unsub-neg 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in z around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-frac-neg2 71.5%

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

   8. Simplified 71.5%

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

   if -2 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 75.7%

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

   if 4.9999999999999999e-17 < (/.f64 z t) < 5.00000000000000027e31

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate--l+ 87.6%

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

      2. div-sub 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in x around 0 63.8%

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

      1. *-commutative 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in z around 0 63.8%

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

       1. associate-*r/ 87.3%

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

       2. *-commutative 87.3%

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

   11. Simplified 87.3%

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

   if 4.0000000000000003e69 < (/.f64 z t) < 2e208

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in x around 0 84.7%

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

      1. *-commutative 84.7%

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

   8. Simplified 84.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+69} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+208}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+32} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e+32) (not (<= (/ z t) 5e-17)))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+32) || !((z / t) <= 5e-17)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d+32)) .or. (.not. ((z / t) <= 5d-17))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+32) || !((z / t) <= 5e-17)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e+32) or not ((z / t) <= 5e-17):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e+32) || !(Float64(z / t) <= 5e-17))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e+32) || ~(((z / t) <= 5e-17)))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e+32], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-17]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.9999999999999997e32 or 4.9999999999999999e-17 < (/.f64 z t)

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 91.2%

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

   4. Taylor expanded in t around 0 94.5%

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

   if -4.9999999999999997e32 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+32} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -0.00021 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -0.00021) (not (<= (/ z t) 5e-17)))
   (* (- y x) (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -0.00021) || !((z / t) <= 5e-17)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-0.00021d0)) .or. (.not. ((z / t) <= 5d-17))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -0.00021) || !((z / t) <= 5e-17)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -0.00021) or not ((z / t) <= 5e-17):
		tmp = (y - x) * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -0.00021) || !(Float64(z / t) <= 5e-17))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -0.00021) || ~(((z / t) <= 5e-17)))
		tmp = (y - x) * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -0.00021], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-17]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.1000000000000001e-4 or 4.9999999999999999e-17 < (/.f64 z t)

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

      2. sub-div 91.6%

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

      3. associate-/r/ 96.7%

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

      4. clear-num 96.6%

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

      5. associate-/l/ 92.7%

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

   5. Applied egg-rr 92.7%

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

      1. associate-/r/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*r* 96.2%

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

      4. associate-/r/ 96.2%

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

      5. clear-num 96.2%

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

   7. Applied egg-rr 96.2%

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

   if -2.1000000000000001e-4 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. unsub-neg 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -0.00021 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5000000.0) (not (<= (/ z t) 5e-17)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5000000.0) || !((z / t) <= 5e-17)) {
		tmp = (y - x) * (z / 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) <= (-5000000.0d0)) .or. (.not. ((z / t) <= 5d-17))) then
        tmp = (y - x) * (z / 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) <= -5000000.0) || !((z / t) <= 5e-17)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5000000.0) or not ((z / t) <= 5e-17):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5000000.0) || !(Float64(z / t) <= 5e-17))
		tmp = Float64(Float64(y - x) * Float64(z / 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) <= -5000000.0) || ~(((z / t) <= 5e-17)))
		tmp = (y - x) * (z / 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], -5000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-17]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / 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) < -5e6 or 4.9999999999999999e-17 < (/.f64 z t)

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. sub-div 92.0%

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

      3. associate-/r/ 97.3%

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

      4. clear-num 97.2%

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

      5. associate-/l/ 93.9%

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

   5. Applied egg-rr 93.9%

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

      1. associate-/r/ 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*r* 96.7%

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

      4. associate-/r/ 96.8%

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

      5. clear-num 96.8%

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

   7. Applied egg-rr 96.8%

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

   if -5e6 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf 93.5%

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

      1. associate-*r/ 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5000000.0) (not (<= (/ z t) 5e-17)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5000000.0) || !((z / t) <= 5e-17)) {
		tmp = (y - x) / (t / z);
	} 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) <= (-5000000.0d0)) .or. (.not. ((z / t) <= 5d-17))) then
        tmp = (y - x) / (t / z)
    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) <= -5000000.0) || !((z / t) <= 5e-17)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5000000.0) or not ((z / t) <= 5e-17):
		tmp = (y - x) / (t / z)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5000000.0) || !(Float64(z / t) <= 5e-17))
		tmp = Float64(Float64(y - x) / Float64(t / z));
	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) <= -5000000.0) || ~(((z / t) <= 5e-17)))
		tmp = (y - x) / (t / z);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-17]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5e6 or 4.9999999999999999e-17 < (/.f64 z t)

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. sub-div 92.0%

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

      3. associate-/r/ 97.3%

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

   5. Applied egg-rr 97.3%

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

   if -5e6 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf 93.5%

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

      1. associate-*r/ 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -0.00021 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -0.00021) (not (<= (/ z t) 5e-17))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -0.00021) || !((z / t) <= 5e-17)) {
		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) <= (-0.00021d0)) .or. (.not. ((z / t) <= 5d-17))) 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) <= -0.00021) || !((z / t) <= 5e-17)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -0.00021) or not ((z / t) <= 5e-17):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -0.00021) || !(Float64(z / t) <= 5e-17))
		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) <= -0.00021) || ~(((z / t) <= 5e-17)))
		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], -0.00021], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-17]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.1000000000000001e-4 or 4.9999999999999999e-17 < (/.f64 z t)

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 89.2%

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

      1. associate--l+ 89.2%

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

      2. div-sub 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x around 0 52.2%

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

      1. *-commutative 52.2%

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

   8. Simplified 52.2%

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

   9. Taylor expanded in z around 0 52.2%

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

       1. associate-*r/ 55.8%

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

       2. *-commutative 55.8%

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

   11. Simplified 55.8%

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

   if -2.1000000000000001e-4 < (/.f64 z t) < 4.9999999999999999e-17

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 76.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -0.00021 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-80} \lor \neg \left(x \leq 5.5 \cdot 10^{-121}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.7e-80) (not (<= x 5.5e-121)))
   (* x (- 1.0 (/ z t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.7e-80) || !(x <= 5.5e-121)) {
		tmp = x * (1.0 - (z / t));
	} 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 ((x <= (-5.7d-80)) .or. (.not. (x <= 5.5d-121))) then
        tmp = x * (1.0d0 - (z / t))
    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 ((x <= -5.7e-80) || !(x <= 5.5e-121)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.7e-80) or not (x <= 5.5e-121):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.7e-80) || !(x <= 5.5e-121))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.7e-80) || ~((x <= 5.5e-121)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.7e-80], N[Not[LessEqual[x, 5.5e-121]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6999999999999999e-80 or 5.50000000000000031e-121 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   5. Simplified 86.9%

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

   if -5.6999999999999999e-80 < x < 5.50000000000000031e-121

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 93.9%

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

      1. associate--l+ 93.9%

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

      2. div-sub 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. *-commutative 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-80} \lor \neg \left(x \leq 5.5 \cdot 10^{-121}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-34} \lor \neg \left(z \leq 6.2 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e-34) (not (<= z 6.2e+16))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-34) || !(z <= 6.2e+16)) {
		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 <= (-2.2d-34)) .or. (.not. (z <= 6.2d+16))) 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 <= -2.2e-34) || !(z <= 6.2e+16)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e-34) or not (z <= 6.2e+16):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e-34) || !(z <= 6.2e+16))
		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 <= -2.2e-34) || ~((z <= 6.2e+16)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e-34], N[Not[LessEqual[z, 6.2e+16]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-34 or 6.2e16 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 84.8%

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

   4. Taylor expanded in y around inf 53.0%

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

   if -2.1999999999999999e-34 < z < 6.2e16

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 65.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-34} \lor \neg \left(z \leq 6.2 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

3. Final simplification 97.3%

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

Alternative 12: 38.2% 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 39.2%

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

4. Final simplification 39.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.3% 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 2024078 
(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))))