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

Percentage Accurate: 97.7% → 97.7%

Time: 5.6s

Alternatives: 9

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

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 97.8%

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

2. Final simplification 97.8%

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

Alternative 2: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := \frac{-z}{\frac{t}{x}}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))) (t_2 (/ (- z) (/ t x))))
   (if (<= (/ z t) -1e+119)
     (* x (/ (- z) t))
     (if (<= (/ z t) -5e+76)
       t_1
       (if (<= (/ z t) -1e+46)
         t_2
         (if (<= (/ z t) -5e-43)
           t_1
           (if (<= (/ z t) 2e-12)
             x
             (if (<= (/ z t) 5e+140) (* z (/ y t)) t_2))))))))

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) <= -1e+119) {
		tmp = x * (-z / t);
	} else if ((z / t) <= -5e+76) {
		tmp = t_1;
	} else if ((z / t) <= -1e+46) {
		tmp = t_2;
	} else if ((z / t) <= -5e-43) {
		tmp = t_1;
	} else if ((z / t) <= 2e-12) {
		tmp = x;
	} else if ((z / t) <= 5e+140) {
		tmp = z * (y / 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 * (z / t)
    t_2 = -z / (t / x)
    if ((z / t) <= (-1d+119)) then
        tmp = x * (-z / t)
    else if ((z / t) <= (-5d+76)) then
        tmp = t_1
    else if ((z / t) <= (-1d+46)) then
        tmp = t_2
    else if ((z / t) <= (-5d-43)) then
        tmp = t_1
    else if ((z / t) <= 2d-12) then
        tmp = x
    else if ((z / t) <= 5d+140) then
        tmp = z * (y / 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 * (z / t);
	double t_2 = -z / (t / x);
	double tmp;
	if ((z / t) <= -1e+119) {
		tmp = x * (-z / t);
	} else if ((z / t) <= -5e+76) {
		tmp = t_1;
	} else if ((z / t) <= -1e+46) {
		tmp = t_2;
	} else if ((z / t) <= -5e-43) {
		tmp = t_1;
	} else if ((z / t) <= 2e-12) {
		tmp = x;
	} else if ((z / t) <= 5e+140) {
		tmp = z * (y / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	t_2 = -z / (t / x)
	tmp = 0
	if (z / t) <= -1e+119:
		tmp = x * (-z / t)
	elif (z / t) <= -5e+76:
		tmp = t_1
	elif (z / t) <= -1e+46:
		tmp = t_2
	elif (z / t) <= -5e-43:
		tmp = t_1
	elif (z / t) <= 2e-12:
		tmp = x
	elif (z / t) <= 5e+140:
		tmp = z * (y / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	t_2 = Float64(Float64(-z) / Float64(t / x))
	tmp = 0.0
	if (Float64(z / t) <= -1e+119)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (Float64(z / t) <= -5e+76)
		tmp = t_1;
	elseif (Float64(z / t) <= -1e+46)
		tmp = t_2;
	elseif (Float64(z / t) <= -5e-43)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e-12)
		tmp = x;
	elseif (Float64(z / t) <= 5e+140)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = t_2;
	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) <= -1e+119)
		tmp = x * (-z / t);
	elseif ((z / t) <= -5e+76)
		tmp = t_1;
	elseif ((z / t) <= -1e+46)
		tmp = t_2;
	elseif ((z / t) <= -5e-43)
		tmp = t_1;
	elseif ((z / t) <= 2e-12)
		tmp = x;
	elseif ((z / t) <= 5e+140)
		tmp = z * (y / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+119], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+76], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1e+46], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], -5e-43], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e-12], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+140], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -9.99999999999999944e118

   1. Initial program 92.0%

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

   2. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. distribute-lft-out-- 67.3%

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

      5. *-rgt-identity 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in z around inf 51.3%

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

      1. associate-*l/ 67.3%

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

      2. associate-*r* 67.3%

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

      3. neg-mul-1 67.3%

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

      4. *-commutative 67.3%

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

      5. distribute-neg-frac 67.3%

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

   7. Simplified 67.3%

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

   if -9.99999999999999944e118 < (/.f64 z t) < -4.99999999999999991e76 or -9.9999999999999999e45 < (/.f64 z t) < -5.00000000000000019e-43

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. distribute-rgt1-in 86.7%

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

      3. mul-1-neg 86.7%

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

      4. cancel-sign-sub-inv 86.7%

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

      5. associate-*l/ 83.2%

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

      6. unsub-neg 83.2%

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

      7. mul-1-neg 83.2%

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

      8. associate-+l+ 83.2%

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

      9. mul-1-neg 83.2%

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

      10. unsub-neg 83.2%

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

      11. +-commutative 83.2%

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

      12. *-commutative 83.2%

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

      13. associate-/l* 86.5%

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

      14. associate-+r- 86.5%

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

      15. associate-/l* 96.3%

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

      16. div-sub 99.8%

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

      17. associate-/l* 90.1%

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

      18. *-commutative 90.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in y around inf 56.7%

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

      1. associate-*r/ 66.5%

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

   7. Simplified 66.5%

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

   if -4.99999999999999991e76 < (/.f64 z t) < -9.9999999999999999e45 or 5.00000000000000008e140 < (/.f64 z t)

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. distribute-rgt1-in 85.4%

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

      3. mul-1-neg 85.4%

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

      4. cancel-sign-sub-inv 85.4%

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

      5. associate-*l/ 87.7%

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

      6. unsub-neg 87.7%

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

      7. mul-1-neg 87.7%

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

      8. associate-+l+ 87.7%

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

      9. mul-1-neg 87.7%

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

      10. unsub-neg 87.7%

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

      11. +-commutative 87.7%

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

      12. *-commutative 87.7%

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

      13. associate-/l* 87.3%

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

      14. associate-+r- 87.3%

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

      15. associate-/l* 82.3%

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

      16. div-sub 99.0%

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

      17. associate-/l* 96.0%

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

      18. *-commutative 96.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in z around inf 98.0%

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

      1. div-sub 98.0%

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

      2. *-rgt-identity 98.0%

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

      3. associate-*r/ 97.8%

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

      4. associate-*l* 97.8%

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

      5. associate-*l/ 97.9%

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

      6. *-lft-identity 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-/l* 71.5%

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

   10. Simplified 71.5%

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

   if -5.00000000000000019e-43 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.9%

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

   if 1.99999999999999996e-12 < (/.f64 z t) < 5.00000000000000008e140

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. distribute-rgt1-in 87.1%

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

      3. mul-1-neg 87.1%

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

      4. cancel-sign-sub-inv 87.1%

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

      5. associate-*l/ 78.6%

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

      6. unsub-neg 78.6%

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

      7. mul-1-neg 78.6%

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

      8. associate-+l+ 78.6%

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

      9. mul-1-neg 78.6%

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

      10. unsub-neg 78.6%

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

      11. +-commutative 78.6%

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

      12. *-commutative 78.6%

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

      13. associate-/l* 87.1%

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

      14. associate-+r- 87.1%

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

      15. associate-/l* 95.2%

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

      16. div-sub 99.5%

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

      17. associate-/l* 87.3%

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

      18. *-commutative 87.3%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 66.8%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.9%

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

   7. Applied egg-rr 77.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+46}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 3: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-43)
   (* y (/ z t))
   (if (<= (/ z t) 2e-12)
     x
     (if (<= (/ z t) 5e+140) (* z (/ y t)) (/ (- z) (/ t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-43) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-12) {
		tmp = x;
	} else if ((z / t) <= 5e+140) {
		tmp = z * (y / t);
	} else {
		tmp = -z / (t / 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-43)) then
        tmp = y * (z / t)
    else if ((z / t) <= 2d-12) then
        tmp = x
    else if ((z / t) <= 5d+140) then
        tmp = z * (y / t)
    else
        tmp = -z / (t / 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-43) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-12) {
		tmp = x;
	} else if ((z / t) <= 5e+140) {
		tmp = z * (y / t);
	} else {
		tmp = -z / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-43:
		tmp = y * (z / t)
	elif (z / t) <= 2e-12:
		tmp = x
	elif (z / t) <= 5e+140:
		tmp = z * (y / t)
	else:
		tmp = -z / (t / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-43)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 2e-12)
		tmp = x;
	elseif (Float64(z / t) <= 5e+140)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = Float64(Float64(-z) / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-43)
		tmp = y * (z / t);
	elseif ((z / t) <= 2e-12)
		tmp = x;
	elseif ((z / t) <= 5e+140)
		tmp = z * (y / t);
	else
		tmp = -z / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-43], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-12], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+140], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 95.9%

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

   2. Taylor expanded in x around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. distribute-rgt1-in 83.1%

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

      3. mul-1-neg 83.1%

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

      4. cancel-sign-sub-inv 83.1%

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

      5. associate-*l/ 82.0%

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

      6. unsub-neg 82.0%

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

      7. mul-1-neg 82.0%

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

      8. associate-+l+ 82.0%

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

      9. mul-1-neg 82.0%

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

      10. unsub-neg 82.0%

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

      11. +-commutative 82.0%

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

      12. *-commutative 82.0%

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

      13. associate-/l* 83.0%

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

      14. associate-+r- 83.0%

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

      15. associate-/l* 84.2%

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

      16. div-sub 95.8%

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

      17. associate-/l* 90.5%

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

      18. *-commutative 90.5%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. associate-*r/ 53.1%

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

   7. Simplified 53.1%

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

   if -5.00000000000000019e-43 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.9%

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

   if 1.99999999999999996e-12 < (/.f64 z t) < 5.00000000000000008e140

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. distribute-rgt1-in 87.1%

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

      3. mul-1-neg 87.1%

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

      4. cancel-sign-sub-inv 87.1%

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

      5. associate-*l/ 78.6%

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

      6. unsub-neg 78.6%

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

      7. mul-1-neg 78.6%

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

      8. associate-+l+ 78.6%

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

      9. mul-1-neg 78.6%

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

      10. unsub-neg 78.6%

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

      11. +-commutative 78.6%

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

      12. *-commutative 78.6%

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

      13. associate-/l* 87.1%

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

      14. associate-+r- 87.1%

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

      15. associate-/l* 95.2%

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

      16. div-sub 99.5%

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

      17. associate-/l* 87.3%

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

      18. *-commutative 87.3%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 66.8%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.9%

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

   7. Applied egg-rr 77.9%

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

   if 5.00000000000000008e140 < (/.f64 z t)

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. distribute-rgt1-in 83.4%

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

      3. mul-1-neg 83.4%

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

      4. cancel-sign-sub-inv 83.4%

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

      5. associate-*l/ 88.2%

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

      6. unsub-neg 88.2%

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

      7. mul-1-neg 88.2%

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

      8. associate-+l+ 88.2%

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

      9. mul-1-neg 88.2%

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

      10. unsub-neg 88.2%

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

      11. +-commutative 88.2%

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

      12. *-commutative 88.2%

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

      13. associate-/l* 85.6%

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

      14. associate-+r- 85.6%

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

      15. associate-/l* 79.9%

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

      16. div-sub 98.9%

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

      17. associate-/l* 97.7%

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

      18. *-commutative 97.7%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. div-sub 97.8%

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

      2. *-rgt-identity 97.8%

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

      3. associate-*r/ 97.6%

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

      4. associate-*l* 97.5%

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

      5. associate-*l/ 97.6%

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

      6. *-lft-identity 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 67.5%

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

   10. Simplified 67.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 4: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -10000000.0)
   (* (- y x) (/ z t))
   (if (<= (/ z t) 2e-12) (+ x (* y (/ z t))) (* z (- (/ y t) (/ x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -10000000.0) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 2e-12) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y / t) - (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) <= (-10000000.0d0)) then
        tmp = (y - x) * (z / t)
    else if ((z / t) <= 2d-12) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y / t) - (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) <= -10000000.0) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 2e-12) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y / t) - (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -10000000.0:
		tmp = (y - x) * (z / t)
	elif (z / t) <= 2e-12:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y / t) - (x / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -10000000.0)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (Float64(z / t) <= 2e-12)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y / t) - Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -10000000.0)
		tmp = (y - x) * (z / t);
	elseif ((z / t) <= 2e-12)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y / t) - (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -10000000.0], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-12], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y / t), $MachinePrecision] - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 95.3%

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

   2. Taylor expanded in x around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. distribute-rgt1-in 83.5%

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

      3. mul-1-neg 83.5%

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

      4. cancel-sign-sub-inv 83.5%

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

      5. associate-*l/ 82.2%

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

      6. unsub-neg 82.2%

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

      7. mul-1-neg 82.2%

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

      8. associate-+l+ 82.2%

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

      9. mul-1-neg 82.2%

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

      10. unsub-neg 82.2%

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

      11. +-commutative 82.2%

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

      12. *-commutative 82.2%

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

      13. associate-/l* 83.3%

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

      14. associate-+r- 83.3%

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

      15. associate-/l* 81.6%

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

      16. div-sub 95.1%

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

      17. associate-/l* 92.1%

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

      18. *-commutative 92.1%

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

   4. Simplified 93.7%

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

   5. Taylor expanded in z around inf 87.5%

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

      1. div-sub 92.6%

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

      2. *-rgt-identity 92.6%

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

      3. associate-*r/ 92.4%

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

      4. associate-*l* 93.1%

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

      5. associate-*l/ 93.2%

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

      6. *-lft-identity 93.2%

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

   7. Simplified 93.2%

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

   if -1e7 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf 96.0%

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

      1. associate-*r/ 98.5%

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

   4. Simplified 98.5%

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

   if 1.99999999999999996e-12 < (/.f64 z t)

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 97.6%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \end{array} \]

Alternative 5: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-43) (not (<= (/ z t) 2e-12))) (* (- y x) (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-43) || !((z / t) <= 2e-12)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d-43)) .or. (.not. ((z / t) <= 2d-12))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-43) || !((z / t) <= 2e-12)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-43) or not ((z / t) <= 2e-12):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-43) || !(Float64(z / t) <= 2e-12))
		tmp = Float64(Float64(y - x) * 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-43) || ~(((z / t) <= 2e-12)))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-43], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-12]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.00000000000000019e-43 or 1.99999999999999996e-12 < (/.f64 z t)

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. distribute-rgt1-in 83.9%

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

      3. mul-1-neg 83.9%

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

      4. cancel-sign-sub-inv 83.9%

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

      5. associate-*l/ 83.3%

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

      6. unsub-neg 83.3%

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

      7. mul-1-neg 83.3%

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

      8. associate-+l+ 83.3%

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

      9. mul-1-neg 83.3%

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

      10. unsub-neg 83.3%

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

      11. +-commutative 83.3%

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

      12. *-commutative 83.3%

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

      13. associate-/l* 84.5%

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

      14. associate-+r- 84.5%

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

      15. associate-/l* 84.7%

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

      16. div-sub 97.4%

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

      17. associate-/l* 92.2%

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

      18. *-commutative 92.2%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in z around inf 90.5%

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

      1. div-sub 92.8%

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

      2. *-rgt-identity 92.8%

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

      3. associate-*r/ 92.6%

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

      4. associate-*l* 92.9%

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

      5. associate-*l/ 93.1%

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

      6. *-lft-identity 93.1%

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

   7. Simplified 93.1%

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

   if -5.00000000000000019e-43 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 96.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10000000.0) (not (<= (/ z t) 2e-12)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000.0) || !((z / t) <= 2e-12)) {
		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) <= (-10000000.0d0)) .or. (.not. ((z / t) <= 2d-12))) 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) <= -10000000.0) || !((z / t) <= 2e-12)) {
		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) <= -10000000.0) or not ((z / t) <= 2e-12):
		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) <= -10000000.0) || !(Float64(z / t) <= 2e-12))
		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) <= -10000000.0) || ~(((z / t) <= 2e-12)))
		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], -10000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-12]], $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) < -1e7 or 1.99999999999999996e-12 < (/.f64 z t)

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. distribute-rgt1-in 84.1%

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

      3. mul-1-neg 84.1%

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

      4. cancel-sign-sub-inv 84.1%

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

      5. associate-*l/ 83.5%

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

      6. unsub-neg 83.5%

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

      7. mul-1-neg 83.5%

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

      8. associate-+l+ 83.5%

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

      9. mul-1-neg 83.5%

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

      10. unsub-neg 83.5%

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

      11. +-commutative 83.5%

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

      12. *-commutative 83.5%

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

      13. associate-/l* 84.8%

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

      14. associate-+r- 84.8%

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

      15. associate-/l* 83.5%

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

      16. div-sub 97.2%

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

      17. associate-/l* 93.1%

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

      18. *-commutative 93.1%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in z around inf 92.8%

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

      1. div-sub 95.2%

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

      2. *-rgt-identity 95.2%

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

      3. associate-*r/ 95.0%

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

      4. associate-*l* 95.3%

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

      5. associate-*l/ 95.5%

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

      6. *-lft-identity 95.5%

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

   7. Simplified 95.5%

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

   if -1e7 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf 96.0%

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

      1. associate-*r/ 98.5%

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

   4. Simplified 98.5%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-43) (not (<= (/ z t) 2e-12))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-43) || !((z / t) <= 2e-12)) {
		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-43)) .or. (.not. ((z / t) <= 2d-12))) 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-43) || !((z / t) <= 2e-12)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-43) or not ((z / t) <= 2e-12):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-43) || !(Float64(z / t) <= 2e-12))
		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-43) || ~(((z / t) <= 2e-12)))
		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-43], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-12]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.00000000000000019e-43 or 1.99999999999999996e-12 < (/.f64 z t)

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. distribute-rgt1-in 83.9%

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

      3. mul-1-neg 83.9%

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

      4. cancel-sign-sub-inv 83.9%

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

      5. associate-*l/ 83.3%

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

      6. unsub-neg 83.3%

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

      7. mul-1-neg 83.3%

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

      8. associate-+l+ 83.3%

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

      9. mul-1-neg 83.3%

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

      10. unsub-neg 83.3%

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

      11. +-commutative 83.3%

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

      12. *-commutative 83.3%

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

      13. associate-/l* 84.5%

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

      14. associate-+r- 84.5%

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

      15. associate-/l* 84.7%

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

      16. div-sub 97.4%

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

      17. associate-/l* 92.2%

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

      18. *-commutative 92.2%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in y around inf 52.1%

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

      1. associate-*r/ 56.2%

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

   7. Simplified 56.2%

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

   if -5.00000000000000019e-43 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-43)
   (* y (/ z t))
   (if (<= (/ z t) 2e-12) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-43) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-12) {
		tmp = x;
	} 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 ((z / t) <= (-5d-43)) then
        tmp = y * (z / t)
    else if ((z / t) <= 2d-12) then
        tmp = x
    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 ((z / t) <= -5e-43) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-12) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-43:
		tmp = y * (z / t)
	elif (z / t) <= 2e-12:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-43)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 2e-12)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-43)
		tmp = y * (z / t);
	elseif ((z / t) <= 2e-12)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-43], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-12], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 95.9%

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

   2. Taylor expanded in x around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. distribute-rgt1-in 83.1%

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

      3. mul-1-neg 83.1%

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

      4. cancel-sign-sub-inv 83.1%

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

      5. associate-*l/ 82.0%

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

      6. unsub-neg 82.0%

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

      7. mul-1-neg 82.0%

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

      8. associate-+l+ 82.0%

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

      9. mul-1-neg 82.0%

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

      10. unsub-neg 82.0%

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

      11. +-commutative 82.0%

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

      12. *-commutative 82.0%

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

      13. associate-/l* 83.0%

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

      14. associate-+r- 83.0%

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

      15. associate-/l* 84.2%

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

      16. div-sub 95.8%

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

      17. associate-/l* 90.5%

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

      18. *-commutative 90.5%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. associate-*r/ 53.1%

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

   7. Simplified 53.1%

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

   if -5.00000000000000019e-43 < (/.f64 z t) < 1.99999999999999996e-12

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.9%

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

   if 1.99999999999999996e-12 < (/.f64 z t)

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. distribute-rgt1-in 84.7%

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

      3. mul-1-neg 84.7%

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

      4. cancel-sign-sub-inv 84.7%

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

      5. associate-*l/ 84.8%

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

      6. unsub-neg 84.8%

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

      7. mul-1-neg 84.8%

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

      8. associate-+l+ 84.8%

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

      9. mul-1-neg 84.8%

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

      10. unsub-neg 84.8%

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

      11. +-commutative 84.8%

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

      12. *-commutative 84.8%

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

      13. associate-/l* 86.1%

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

      14. associate-+r- 86.1%

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

      15. associate-/l* 85.3%

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

      16. div-sub 99.1%

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

      17. associate-/l* 94.0%

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

      18. *-commutative 94.0%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. associate-*r/ 59.5%

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

   7. Simplified 59.5%

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

      1. associate-*r/ 54.1%

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

      2. associate-/l* 60.3%

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

   9. Applied egg-rr 60.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 38.7% 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 97.8%

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

2. Taylor expanded in z around 0 40.8%

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

3. Final simplification 40.8%

   \[\leadsto x \]

Developer target: 97.6% 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 2023187 
(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))))