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

Percentage Accurate: 97.4% → 98.3%

Time: 9.0s

Alternatives: 14

Speedup: 0.5×

• 24.3% 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: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (* (- y x) (/ z t))) 4e+306)
   (+ x (/ (- y x) (/ t z)))
   (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + ((y - x) * (z / t))) <= 4e+306) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + ((y - x) * (z / t))) <= 4d+306) then
        tmp = x + ((y - x) / (t / z))
    else
        tmp = ((y - x) * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + ((y - x) * (z / t))) <= 4e+306) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + ((y - x) * (z / t))) <= 4e+306:
		tmp = x + ((y - x) / (t / z))
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y - x) * Float64(z / t))) <= 4e+306)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + ((y - x) * (z / t))) <= 4e+306)
		tmp = x + ((y - x) / (t / z));
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e+306], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 4.00000000000000007e306

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.1%

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

   3. Applied egg-rr 98.1%

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

   if 4.00000000000000007e306 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 84.7%

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

   2. Taylor expanded in z around inf 97.2%

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

   3. Taylor expanded in t around inf 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 61.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215} \lor \neg \left(\frac{z}{t} \leq 10^{+272}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- x) t))))
   (if (<= (/ z t) -2e+224)
     t_1
     (if (<= (/ z t) -5e-70)
       (/ y (/ t z))
       (if (<= (/ z t) 1e-105)
         x
         (if (<= (/ z t) 5e+22)
           (* y (/ z t))
           (if (or (<= (/ z t) 5e+215) (not (<= (/ z t) 1e+272)))
             t_1
             (* z (/ y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (-x / t);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_1;
	} else if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e-105) {
		tmp = x;
	} else if ((z / t) <= 5e+22) {
		tmp = y * (z / t);
	} else if (((z / t) <= 5e+215) || !((z / t) <= 1e+272)) {
		tmp = t_1;
	} else {
		tmp = z * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = z * (-x / t)
    if ((z / t) <= (-2d+224)) then
        tmp = t_1
    else if ((z / t) <= (-5d-70)) then
        tmp = y / (t / z)
    else if ((z / t) <= 1d-105) then
        tmp = x
    else if ((z / t) <= 5d+22) then
        tmp = y * (z / t)
    else if (((z / t) <= 5d+215) .or. (.not. ((z / t) <= 1d+272))) then
        tmp = t_1
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (-x / t);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_1;
	} else if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e-105) {
		tmp = x;
	} else if ((z / t) <= 5e+22) {
		tmp = y * (z / t);
	} else if (((z / t) <= 5e+215) || !((z / t) <= 1e+272)) {
		tmp = t_1;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (-x / t)
	tmp = 0
	if (z / t) <= -2e+224:
		tmp = t_1
	elif (z / t) <= -5e-70:
		tmp = y / (t / z)
	elif (z / t) <= 1e-105:
		tmp = x
	elif (z / t) <= 5e+22:
		tmp = y * (z / t)
	elif ((z / t) <= 5e+215) or not ((z / t) <= 1e+272):
		tmp = t_1
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(-x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -2e+224)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e-70)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 1e-105)
		tmp = x;
	elseif (Float64(z / t) <= 5e+22)
		tmp = Float64(y * Float64(z / t));
	elseif ((Float64(z / t) <= 5e+215) || !(Float64(z / t) <= 1e+272))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (-x / t);
	tmp = 0.0;
	if ((z / t) <= -2e+224)
		tmp = t_1;
	elseif ((z / t) <= -5e-70)
		tmp = y / (t / z);
	elseif ((z / t) <= 1e-105)
		tmp = x;
	elseif ((z / t) <= 5e+22)
		tmp = y * (z / t);
	elseif (((z / t) <= 5e+215) || ~(((z / t) <= 1e+272)))
		tmp = t_1;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+224], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-105], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+22], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z / t), $MachinePrecision], 5e+215], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e+272]], $MachinePrecision]], t$95$1, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -1.99999999999999994e224 or 4.9999999999999996e22 < (/.f64 z t) < 5.0000000000000001e215 or 1.0000000000000001e272 < (/.f64 z t)

   1. Initial program 92.4%

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

   2. Taylor expanded in z around inf 96.4%

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

   3. Taylor expanded in y around 0 69.7%

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

      1. neg-mul-1 69.7%

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

      2. distribute-neg-frac 69.7%

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

   5. Simplified 69.7%

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

   if -1.99999999999999994e224 < (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 83.4%

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

   3. Taylor expanded in y around 0 83.4%

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

      1. neg-mul-1 83.4%

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

      2. +-commutative 83.4%

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

      3. sub-neg 83.4%

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

      4. div-sub 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around inf 51.4%

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

      1. associate-/l* 60.8%

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

   8. Simplified 60.8%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 9.99999999999999965e-106

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 85.5%

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

   if 9.99999999999999965e-106 < (/.f64 z t) < 4.9999999999999996e22

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 57.1%

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

   3. Taylor expanded in y around 0 57.1%

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

      1. neg-mul-1 57.1%

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

      2. +-commutative 57.1%

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

      3. sub-neg 57.1%

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

      4. div-sub 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y around inf 43.0%

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

      1. associate-/l* 61.2%

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

   8. Simplified 61.2%

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

      1. clear-num 61.1%

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

      2. associate-/r/ 61.2%

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

      3. clear-num 61.2%

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

   10. Applied egg-rr 61.2%

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

   if 5.0000000000000001e215 < (/.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 80.0%

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

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215} \lor \neg \left(\frac{z}{t} \leq 10^{+272}\right):\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 61.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- x) t))))
   (if (<= (/ z t) -2e+224)
     t_1
     (if (<= (/ z t) -5e-70)
       (/ y (/ t z))
       (if (<= (/ z t) 1e-105)
         x
         (if (<= (/ z t) 5e+22)
           (* y (/ z t))
           (if (<= (/ z t) 5e+215)
             t_1
             (if (<= (/ z t) 1e+272) (* z (/ y t)) (/ (- z) (/ t x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (-x / t);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_1;
	} else if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e-105) {
		tmp = x;
	} else if ((z / t) <= 5e+22) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e+215) {
		tmp = t_1;
	} else if ((z / t) <= 1e+272) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (-x / t)
    if ((z / t) <= (-2d+224)) then
        tmp = t_1
    else if ((z / t) <= (-5d-70)) then
        tmp = y / (t / z)
    else if ((z / t) <= 1d-105) then
        tmp = x
    else if ((z / t) <= 5d+22) then
        tmp = y * (z / t)
    else if ((z / t) <= 5d+215) then
        tmp = t_1
    else if ((z / t) <= 1d+272) 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 t_1 = z * (-x / t);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_1;
	} else if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e-105) {
		tmp = x;
	} else if ((z / t) <= 5e+22) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e+215) {
		tmp = t_1;
	} else if ((z / t) <= 1e+272) {
		tmp = z * (y / t);
	} else {
		tmp = -z / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (-x / t)
	tmp = 0
	if (z / t) <= -2e+224:
		tmp = t_1
	elif (z / t) <= -5e-70:
		tmp = y / (t / z)
	elif (z / t) <= 1e-105:
		tmp = x
	elif (z / t) <= 5e+22:
		tmp = y * (z / t)
	elif (z / t) <= 5e+215:
		tmp = t_1
	elif (z / t) <= 1e+272:
		tmp = z * (y / t)
	else:
		tmp = -z / (t / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(-x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -2e+224)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e-70)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 1e-105)
		tmp = x;
	elseif (Float64(z / t) <= 5e+22)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 5e+215)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e+272)
		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)
	t_1 = z * (-x / t);
	tmp = 0.0;
	if ((z / t) <= -2e+224)
		tmp = t_1;
	elseif ((z / t) <= -5e-70)
		tmp = y / (t / z);
	elseif ((z / t) <= 1e-105)
		tmp = x;
	elseif ((z / t) <= 5e+22)
		tmp = y * (z / t);
	elseif ((z / t) <= 5e+215)
		tmp = t_1;
	elseif ((z / t) <= 1e+272)
		tmp = z * (y / t);
	else
		tmp = -z / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+224], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-105], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+22], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e+215], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e+272], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 z t) < -1.99999999999999994e224 or 4.9999999999999996e22 < (/.f64 z t) < 5.0000000000000001e215

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 94.9%

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

   3. Taylor expanded in y around 0 72.8%

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

      1. neg-mul-1 72.8%

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

      2. distribute-neg-frac 72.8%

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

   5. Simplified 72.8%

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

   if -1.99999999999999994e224 < (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 83.4%

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

   3. Taylor expanded in y around 0 83.4%

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

      1. neg-mul-1 83.4%

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

      2. +-commutative 83.4%

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

      3. sub-neg 83.4%

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

      4. div-sub 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around inf 51.4%

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

      1. associate-/l* 60.8%

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

   8. Simplified 60.8%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 9.99999999999999965e-106

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 85.5%

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

   if 9.99999999999999965e-106 < (/.f64 z t) < 4.9999999999999996e22

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 57.1%

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

   3. Taylor expanded in y around 0 57.1%

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

      1. neg-mul-1 57.1%

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

      2. +-commutative 57.1%

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

      3. sub-neg 57.1%

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

      4. div-sub 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y around inf 43.0%

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

      1. associate-/l* 61.2%

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

   8. Simplified 61.2%

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

      1. clear-num 61.1%

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

      2. associate-/r/ 61.2%

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

      3. clear-num 61.2%

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

   10. Applied egg-rr 61.2%

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

   if 5.0000000000000001e215 < (/.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 80.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if 1.0000000000000001e272 < (/.f64 z t)

   1. Initial program 82.5%

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

   2. Taylor expanded in z around inf 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-/l* 62.6%

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

      3. distribute-neg-frac 62.6%

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

   8. Simplified 62.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 4: 61.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+224)
   (/ (* x (- z)) t)
   (if (<= (/ z t) -5e-70)
     (/ y (/ t z))
     (if (<= (/ z t) 1e-105)
       x
       (if (<= (/ z t) 5e+22)
         (* y (/ z t))
         (if (<= (/ z t) 5e+215)
           (* z (/ (- x) t))
           (if (<= (/ z t) 1e+272) (* z (/ y t)) (/ (- z) (/ t x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e-105) {
		tmp = x;
	} else if ((z / t) <= 5e+22) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e+215) {
		tmp = z * (-x / t);
	} else if ((z / t) <= 1e+272) {
		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) <= (-2d+224)) then
        tmp = (x * -z) / t
    else if ((z / t) <= (-5d-70)) then
        tmp = y / (t / z)
    else if ((z / t) <= 1d-105) then
        tmp = x
    else if ((z / t) <= 5d+22) then
        tmp = y * (z / t)
    else if ((z / t) <= 5d+215) then
        tmp = z * (-x / t)
    else if ((z / t) <= 1d+272) 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) <= -2e+224) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 1e-105) {
		tmp = x;
	} else if ((z / t) <= 5e+22) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e+215) {
		tmp = z * (-x / t);
	} else if ((z / t) <= 1e+272) {
		tmp = z * (y / t);
	} else {
		tmp = -z / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+224:
		tmp = (x * -z) / t
	elif (z / t) <= -5e-70:
		tmp = y / (t / z)
	elif (z / t) <= 1e-105:
		tmp = x
	elif (z / t) <= 5e+22:
		tmp = y * (z / t)
	elif (z / t) <= 5e+215:
		tmp = z * (-x / t)
	elif (z / t) <= 1e+272:
		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) <= -2e+224)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (Float64(z / t) <= -5e-70)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 1e-105)
		tmp = x;
	elseif (Float64(z / t) <= 5e+22)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 5e+215)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (Float64(z / t) <= 1e+272)
		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) <= -2e+224)
		tmp = (x * -z) / t;
	elseif ((z / t) <= -5e-70)
		tmp = y / (t / z);
	elseif ((z / t) <= 1e-105)
		tmp = x;
	elseif ((z / t) <= 5e+22)
		tmp = y * (z / t);
	elseif ((z / t) <= 5e+215)
		tmp = z * (-x / t);
	elseif ((z / t) <= 1e+272)
		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], -2e+224], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-105], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+22], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e+215], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+272], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if (/.f64 z t) < -1.99999999999999994e224

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 92.7%

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

   3. Taylor expanded in y around 0 92.7%

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

      1. neg-mul-1 92.7%

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

      2. +-commutative 92.7%

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

      3. sub-neg 92.7%

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

      4. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. mul-1-neg 71.8%

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

      3. distribute-rgt-neg-out 71.8%

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

   8. Simplified 71.8%

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

   if -1.99999999999999994e224 < (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 83.4%

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

   3. Taylor expanded in y around 0 83.4%

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

      1. neg-mul-1 83.4%

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

      2. +-commutative 83.4%

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

      3. sub-neg 83.4%

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

      4. div-sub 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around inf 51.4%

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

      1. associate-/l* 60.8%

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

   8. Simplified 60.8%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 9.99999999999999965e-106

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 85.5%

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

   if 9.99999999999999965e-106 < (/.f64 z t) < 4.9999999999999996e22

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 57.1%

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

   3. Taylor expanded in y around 0 57.1%

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

      1. neg-mul-1 57.1%

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

      2. +-commutative 57.1%

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

      3. sub-neg 57.1%

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

      4. div-sub 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y around inf 43.0%

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

      1. associate-/l* 61.2%

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

   8. Simplified 61.2%

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

      1. clear-num 61.1%

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

      2. associate-/r/ 61.2%

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

      3. clear-num 61.2%

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

   10. Applied egg-rr 61.2%

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

   if 4.9999999999999996e22 < (/.f64 z t) < 5.0000000000000001e215

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 96.7%

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

   3. Taylor expanded in y around 0 73.8%

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

      1. neg-mul-1 73.8%

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

      2. distribute-neg-frac 73.8%

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

   5. Simplified 73.8%

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

   if 5.0000000000000001e215 < (/.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 80.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if 1.0000000000000001e272 < (/.f64 z t)

   1. Initial program 82.5%

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

   2. Taylor expanded in z around inf 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-/l* 62.6%

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

      3. distribute-neg-frac 62.6%

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

   8. Simplified 62.6%

      \[\leadsto \color{blue}{\frac{-z}{\frac{t}{x}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (<= t_1 4e+306) t_1 (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 4e+306) {
		tmp = t_1;
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / t))
    if (t_1 <= 4d+306) then
        tmp = t_1
    else
        tmp = ((y - x) * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 4e+306) {
		tmp = t_1;
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - x) * (z / t))
	tmp = 0
	if t_1 <= 4e+306:
		tmp = t_1
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / t)))
	tmp = 0.0
	if (t_1 <= 4e+306)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - x) * (z / t));
	tmp = 0.0;
	if (t_1 <= 4e+306)
		tmp = t_1;
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+306], t$95$1, N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 4.00000000000000007e306

   1. Initial program 98.1%

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

   if 4.00000000000000007e306 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 84.7%

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

   2. Taylor expanded in z around inf 97.2%

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

   3. Taylor expanded in t around inf 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 6: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70} \lor \neg \left(\frac{z}{t} \leq 10^{-105}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-70) (not (<= (/ z t) 1e-105))) (* (- y x) (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-70) || !((z / t) <= 1e-105)) {
		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-70)) .or. (.not. ((z / t) <= 1d-105))) 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-70) || !((z / t) <= 1e-105)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-70) or not ((z / t) <= 1e-105):
		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-70) || !(Float64(z / t) <= 1e-105))
		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-70) || ~(((z / t) <= 1e-105)))
		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-70], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-105]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.9999999999999998e-70 or 9.99999999999999965e-106 < (/.f64 z t)

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 85.7%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. associate-/l* 87.5%

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

      2. div-inv 87.4%

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

      3. clear-num 87.5%

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

   5. Applied egg-rr 87.5%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 9.99999999999999965e-106

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 85.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70} \lor \neg \left(\frac{z}{t} \leq 10^{-105}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-70)
   (* (- y x) (/ z t))
   (if (<= (/ z t) 5e-28) x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-70) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 5e-28) {
		tmp = x;
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-5d-70)) then
        tmp = (y - x) * (z / t)
    else if ((z / t) <= 5d-28) then
        tmp = x
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-70) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 5e-28) {
		tmp = x;
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-70:
		tmp = (y - x) * (z / t)
	elif (z / t) <= 5e-28:
		tmp = x
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-70)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (Float64(z / t) <= 5e-28)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-70)
		tmp = (y - x) * (z / t);
	elseif ((z / t) <= 5e-28)
		tmp = x;
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-28], x, N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 86.8%

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

   3. Taylor expanded in t around inf 84.5%

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

      1. associate-/l* 91.6%

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

      2. div-inv 91.4%

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

      3. clear-num 91.5%

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

   5. Applied egg-rr 91.5%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 5.0000000000000002e-28

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 80.2%

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

   if 5.0000000000000002e-28 < (/.f64 z t)

   1. Initial program 93.6%

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

   2. Taylor expanded in z around inf 94.7%

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

   3. Taylor expanded in y around 0 94.7%

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

      1. neg-mul-1 94.7%

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

      2. +-commutative 94.7%

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

      3. sub-neg 94.7%

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

      4. div-sub 96.1%

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

   5. Simplified 96.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 8: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2.0)
   (* (- y x) (/ z t))
   (if (<= (/ z t) 4e-17) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2.0) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 4e-17) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2.0d0)) then
        tmp = (y - x) * (z / t)
    else if ((z / t) <= 4d-17) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2.0) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 4e-17) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2.0:
		tmp = (y - x) * (z / t)
	elif (z / t) <= 4e-17:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2.0)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (Float64(z / t) <= 4e-17)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2.0)
		tmp = (y - x) * (z / t);
	elseif ((z / t) <= 4e-17)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2.0], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-17], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 91.8%

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

   3. Taylor expanded in t around inf 91.9%

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

      1. associate-/l* 95.9%

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

      2. div-inv 95.7%

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

      3. clear-num 95.8%

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

   5. Applied egg-rr 95.8%

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

   if -2 < (/.f64 z t) < 4.00000000000000029e-17

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. associate-*r/ 97.5%

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

   4. Simplified 97.5%

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

   if 4.00000000000000029e-17 < (/.f64 z t)

   1. Initial program 93.4%

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

   2. Taylor expanded in z around inf 95.8%

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

   3. Taylor expanded in y around 0 95.8%

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

      1. neg-mul-1 95.8%

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

      2. +-commutative 95.8%

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

      3. sub-neg 95.8%

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

      4. div-sub 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 9: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-18}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e-18)
   (/ (- y x) (/ t z))
   (if (<= (/ z t) 4e-17) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-18) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 4e-17) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1d-18)) then
        tmp = (y - x) / (t / z)
    else if ((z / t) <= 4d-17) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-18) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 4e-17) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e-18:
		tmp = (y - x) / (t / z)
	elif (z / t) <= 4e-17:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e-18)
		tmp = Float64(Float64(y - x) / Float64(t / z));
	elseif (Float64(z / t) <= 4e-17)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e-18)
		tmp = (y - x) / (t / z);
	elseif ((z / t) <= 4e-17)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e-18], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-17], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.0000000000000001e-18

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 91.9%

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

      1. sub-div 94.8%

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

      2. associate-/r/ 95.9%

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

   4. Applied egg-rr 95.9%

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

   if -1.0000000000000001e-18 < (/.f64 z t) < 4.00000000000000029e-17

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 94.2%

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

      1. associate-*r/ 97.5%

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

   4. Simplified 97.5%

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

   if 4.00000000000000029e-17 < (/.f64 z t)

   1. Initial program 93.4%

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

   2. Taylor expanded in z around inf 95.8%

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

   3. Taylor expanded in y around 0 95.8%

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

      1. neg-mul-1 95.8%

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

      2. +-commutative 95.8%

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

      3. sub-neg 95.8%

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

      4. div-sub 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-18}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 10: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-70)
   (* y (/ z t))
   (if (<= (/ z t) 5e-48) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-70) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e-48) {
		tmp = x;
	} else {
		tmp = z * (y / 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-70)) then
        tmp = y * (z / t)
    else if ((z / t) <= 5d-48) then
        tmp = x
    else
        tmp = z * (y / 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-70) {
		tmp = y * (z / t);
	} else if ((z / t) <= 5e-48) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-70:
		tmp = y * (z / t)
	elif (z / t) <= 5e-48:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-70)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 5e-48)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-70)
		tmp = y * (z / t);
	elseif ((z / t) <= 5e-48)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-48], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 86.8%

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

   3. Taylor expanded in y around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. +-commutative 86.8%

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

      3. sub-neg 86.8%

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

      4. div-sub 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 56.4%

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

   8. Simplified 56.4%

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

      1. clear-num 56.4%

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

      2. associate-/r/ 56.3%

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

      3. clear-num 56.4%

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

   10. Applied egg-rr 56.4%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 4.9999999999999999e-48

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 80.8%

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

   if 4.9999999999999999e-48 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.5%

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

   3. Taylor expanded in y around inf 51.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-70)
   (/ y (/ t z))
   (if (<= (/ z t) 5e-48) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 5e-48) {
		tmp = x;
	} else {
		tmp = z * (y / 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-70)) then
        tmp = y / (t / z)
    else if ((z / t) <= 5d-48) then
        tmp = x
    else
        tmp = z * (y / 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-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 5e-48) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-70:
		tmp = y / (t / z)
	elif (z / t) <= 5e-48:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-70)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 5e-48)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-70)
		tmp = y / (t / z);
	elseif ((z / t) <= 5e-48)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-48], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 86.8%

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

   3. Taylor expanded in y around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. +-commutative 86.8%

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

      3. sub-neg 86.8%

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

      4. div-sub 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 56.4%

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

   8. Simplified 56.4%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 4.9999999999999999e-48

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 80.8%

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

   if 4.9999999999999999e-48 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.5%

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

   3. Taylor expanded in y around inf 51.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 12: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-70)
   (/ y (/ t z))
   (if (<= (/ z t) 5e-48) x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 5e-48) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	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-70)) then
        tmp = y / (t / z)
    else if ((z / t) <= 5d-48) then
        tmp = x
    else
        tmp = z / (t / y)
    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-70) {
		tmp = y / (t / z);
	} else if ((z / t) <= 5e-48) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-70:
		tmp = y / (t / z)
	elif (z / t) <= 5e-48:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-70)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 5e-48)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-70)
		tmp = y / (t / z);
	elseif ((z / t) <= 5e-48)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-70], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-48], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.9999999999999998e-70

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 86.8%

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

   3. Taylor expanded in y around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. +-commutative 86.8%

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

      3. sub-neg 86.8%

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

      4. div-sub 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 56.4%

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

   8. Simplified 56.4%

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

   if -4.9999999999999998e-70 < (/.f64 z t) < 4.9999999999999999e-48

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 80.8%

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

   if 4.9999999999999999e-48 < (/.f64 z t)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 93.5%

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

   3. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. clear-num 51.2%

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

      3. un-div-inv 51.2%

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

   5. Applied egg-rr 51.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 13: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-107} \lor \neg \left(z \leq 1.1 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e-107) (not (<= z 1.1e-57))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e-107) || !(z <= 1.1e-57)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.5d-107)) .or. (.not. (z <= 1.1d-57))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e-107) || !(z <= 1.1e-57)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e-107) or not (z <= 1.1e-57):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e-107) || !(z <= 1.1e-57))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5e-107) || ~((z <= 1.1e-57)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e-107], N[Not[LessEqual[z, 1.1e-57]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4999999999999999e-107 or 1.09999999999999999e-57 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 83.8%

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

   3. Taylor expanded in y around inf 51.5%

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

   if -1.4999999999999999e-107 < z < 1.09999999999999999e-57

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 69.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-107} \lor \neg \left(z \leq 1.1 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 38.6% 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 96.2%

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

2. Taylor expanded in z around 0 36.5%

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

3. Final simplification 36.5%

   \[\leadsto x \]

Developer target: 97.3% 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 2023279 
(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))))