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

Percentage Accurate: 97.7% → 97.7%

Time: 9.5s

Alternatives: 10

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. +-commutative 98.5%

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

   2. fma-define 98.5%

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

3. Simplified 98.5%

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

Alternative 2: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+91} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{+228}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5.0)
   (/ x (/ t (- z)))
   (if (<= (/ z t) 1e-9)
     x
     (if (or (<= (/ z t) 1e+91) (not (<= (/ z t) 4e+228)))
       (* y (/ z t))
       (* x (/ z (- t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5.0) {
		tmp = x / (t / -z);
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if (((z / t) <= 1e+91) || !((z / t) <= 4e+228)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (z / -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-5.0d0)) then
        tmp = x / (t / -z)
    else if ((z / t) <= 1d-9) then
        tmp = x
    else if (((z / t) <= 1d+91) .or. (.not. ((z / t) <= 4d+228))) then
        tmp = y * (z / t)
    else
        tmp = x * (z / -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5.0) {
		tmp = x / (t / -z);
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if (((z / t) <= 1e+91) || !((z / t) <= 4e+228)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (z / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5.0:
		tmp = x / (t / -z)
	elif (z / t) <= 1e-9:
		tmp = x
	elif ((z / t) <= 1e+91) or not ((z / t) <= 4e+228):
		tmp = y * (z / t)
	else:
		tmp = x * (z / -t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5.0)
		tmp = Float64(x / Float64(t / Float64(-z)));
	elseif (Float64(z / t) <= 1e-9)
		tmp = x;
	elseif ((Float64(z / t) <= 1e+91) || !(Float64(z / t) <= 4e+228))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x * Float64(z / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5.0)
		tmp = x / (t / -z);
	elseif ((z / t) <= 1e-9)
		tmp = x;
	elseif (((z / t) <= 1e+91) || ~(((z / t) <= 4e+228)))
		tmp = y * (z / t);
	else
		tmp = x * (z / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5.0], N[(x / N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-9], x, If[Or[LessEqual[N[(z / t), $MachinePrecision], 1e+91], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e+228]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in z around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. distribute-frac-neg 64.4%

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

   8. Simplified 64.4%

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

      1. distribute-frac-neg 64.4%

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

      2. distribute-rgt-neg-in 64.4%

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

      3. clear-num 64.4%

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

      4. div-inv 64.4%

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

      5. distribute-neg-frac 64.4%

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

   10. Applied egg-rr 64.4%

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

   if -5 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 78.7%

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

   if 1.00000000000000006e-9 < (/.f64 z t) < 1.00000000000000008e91 or 3.9999999999999997e228 < (/.f64 z t)

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. associate-/l* 88.5%

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

      3. distribute-lft-neg-out 88.5%

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

      4. associate-*r/ 92.7%

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

      5. distribute-rgt-in 97.5%

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

      6. +-commutative 97.5%

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

      7. sub-neg 97.5%

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

      8. associate-*l/ 86.3%

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

      9. associate-/l* 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in y around inf 79.1%

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

      1. +-commutative 79.1%

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

      2. mul-1-neg 79.1%

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

      3. unsub-neg 79.1%

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

      4. associate-/l* 81.4%

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

      5. *-commutative 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in x around 0 62.9%

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

       1. associate-*r/ 74.1%

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

   11. Simplified 74.1%

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

   if 1.00000000000000008e91 < (/.f64 z t) < 3.9999999999999997e228

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-frac-neg 76.6%

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

   8. Simplified 76.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+91} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{+228}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ \mathbf{if}\;\frac{z}{t} \leq -5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+91} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{+228}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))))
   (if (<= (/ z t) -5.0)
     t_1
     (if (<= (/ z t) 1e-9)
       x
       (if (or (<= (/ z t) 1e+91) (not (<= (/ z t) 4e+228)))
         (* y (/ z t))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if ((z / t) <= -5.0) {
		tmp = t_1;
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if (((z / t) <= 1e+91) || !((z / t) <= 4e+228)) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / -t)
    if ((z / t) <= (-5.0d0)) then
        tmp = t_1
    else if ((z / t) <= 1d-9) then
        tmp = x
    else if (((z / t) <= 1d+91) .or. (.not. ((z / t) <= 4d+228))) then
        tmp = y * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if ((z / t) <= -5.0) {
		tmp = t_1;
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if (((z / t) <= 1e+91) || !((z / t) <= 4e+228)) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	tmp = 0
	if (z / t) <= -5.0:
		tmp = t_1
	elif (z / t) <= 1e-9:
		tmp = x
	elif ((z / t) <= 1e+91) or not ((z / t) <= 4e+228):
		tmp = y * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	tmp = 0.0
	if (Float64(z / t) <= -5.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-9)
		tmp = x;
	elseif ((Float64(z / t) <= 1e+91) || !(Float64(z / t) <= 4e+228))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	tmp = 0.0;
	if ((z / t) <= -5.0)
		tmp = t_1;
	elseif ((z / t) <= 1e-9)
		tmp = x;
	elseif (((z / t) <= 1e+91) || ~(((z / t) <= 4e+228)))
		tmp = y * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-9], x, If[Or[LessEqual[N[(z / t), $MachinePrecision], 1e+91], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e+228]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -5 or 1.00000000000000008e91 < (/.f64 z t) < 3.9999999999999997e228

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-frac-neg 67.2%

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

   8. Simplified 67.2%

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

   if -5 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 78.7%

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

   if 1.00000000000000006e-9 < (/.f64 z t) < 1.00000000000000008e91 or 3.9999999999999997e228 < (/.f64 z t)

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. associate-/l* 88.5%

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

      3. distribute-lft-neg-out 88.5%

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

      4. associate-*r/ 92.7%

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

      5. distribute-rgt-in 97.5%

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

      6. +-commutative 97.5%

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

      7. sub-neg 97.5%

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

      8. associate-*l/ 86.3%

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

      9. associate-/l* 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in y around inf 79.1%

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

      1. +-commutative 79.1%

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

      2. mul-1-neg 79.1%

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

      3. unsub-neg 79.1%

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

      4. associate-/l* 81.4%

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

      5. *-commutative 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in x around 0 62.9%

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

       1. associate-*r/ 74.1%

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

   11. Simplified 74.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+91} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{+228}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-11} \lor \neg \left(\frac{z}{t} \leq 10^{-9}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-11) (not (<= (/ z t) 1e-9))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-11) || !((z / t) <= 1e-9)) {
		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-11)) .or. (.not. ((z / t) <= 1d-9))) 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-11) || !((z / t) <= 1e-9)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-11) or not ((z / t) <= 1e-9):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-11) || !(Float64(z / t) <= 1e-9))
		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-11) || ~(((z / t) <= 1e-9)))
		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-11], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-9]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.00000000000000018e-11 or 1.00000000000000006e-9 < (/.f64 z t)

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 88.8%

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

      1. mul-1-neg 88.8%

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

      2. associate-/l* 90.2%

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

      3. distribute-lft-neg-out 90.2%

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

      4. associate-*r/ 89.5%

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

      5. distribute-rgt-in 97.8%

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

      6. +-commutative 97.8%

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

      7. sub-neg 97.8%

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

      8. associate-*l/ 92.5%

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

      9. associate-/l* 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in y around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. associate-/l* 72.9%

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

      5. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in x around 0 51.1%

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

       1. associate-*r/ 55.3%

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

   11. Simplified 55.3%

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

   if -5.00000000000000018e-11 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 79.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-11} \lor \neg \left(\frac{z}{t} \leq 10^{-9}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -200000000000.0)
   (* z (- (/ x t)))
   (if (<= (/ z t) 1e-9) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = z * -(x / t);
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-200000000000.0d0)) then
        tmp = z * -(x / t)
    else if ((z / t) <= 1d-9) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = z * -(x / t);
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -200000000000.0:
		tmp = z * -(x / t)
	elif (z / t) <= 1e-9:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -200000000000.0)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (Float64(z / t) <= 1e-9)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -200000000000.0)
		tmp = z * -(x / t);
	elseif ((z / t) <= 1e-9)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -200000000000.0], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-9], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in z around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-frac-neg 65.9%

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

   8. Simplified 65.9%

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

      1. distribute-frac-neg 65.9%

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

      2. distribute-rgt-neg-in 65.9%

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

      3. clear-num 66.0%

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

      4. div-inv 66.0%

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

      5. associate-/r/ 61.0%

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

   10. Applied egg-rr 61.0%

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

   if -2e11 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 77.5%

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

   if 1.00000000000000006e-9 < (/.f64 z t)

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. associate-/l* 89.2%

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

      3. distribute-lft-neg-out 89.2%

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

      4. associate-*r/ 95.1%

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

      5. distribute-rgt-in 98.3%

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

      6. +-commutative 98.3%

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

      7. sub-neg 98.3%

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

      8. associate-*l/ 87.8%

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

      9. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in y around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. associate-/l* 76.9%

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

      5. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in x around 0 52.0%

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

       1. associate-*r/ 61.0%

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

   11. Simplified 61.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-13} \lor \neg \left(y \leq 2.7 \cdot 10^{-132}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.7e-13) (not (<= y 2.7e-132)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.7e-13) || !(y <= 2.7e-132)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.7d-13)) .or. (.not. (y <= 2.7d-132))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.7e-13) || !(y <= 2.7e-132)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.7e-13) or not (y <= 2.7e-132):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.7e-13) || !(y <= 2.7e-132))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.7e-13) || ~((y <= 2.7e-132)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.7e-13], N[Not[LessEqual[y, 2.7e-132]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999989e-13 or 2.6999999999999999e-132 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 89.0%

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

      1. associate-*r/ 92.3%

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

   5. Simplified 92.3%

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

   if -3.69999999999999989e-13 < y < 2.6999999999999999e-132

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. unsub-neg 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-13} \lor \neg \left(y \leq 2.7 \cdot 10^{-132}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+83} \lor \neg \left(y \leq 10^{+202}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.7e+83) (not (<= y 1e+202)))
   (* y (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e+83) || !(y <= 1e+202)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.7d+83)) .or. (.not. (y <= 1d+202))) then
        tmp = y * (z / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e+83) || !(y <= 1e+202)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.7e+83) or not (y <= 1e+202):
		tmp = y * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.7e+83) || !(y <= 1e+202))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.7e+83) || ~((y <= 1e+202)))
		tmp = y * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.7e+83], N[Not[LessEqual[y, 1e+202]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6999999999999999e83 or 9.999999999999999e201 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.6%

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

      1. mul-1-neg 88.6%

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

      2. associate-/l* 88.6%

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

      3. distribute-lft-neg-out 88.6%

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

      4. associate-*r/ 94.6%

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

      5. distribute-rgt-in 99.0%

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

      6. +-commutative 99.0%

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

      7. sub-neg 99.0%

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

      8. associate-*l/ 93.0%

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

      9. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in y around inf 96.0%

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

      1. +-commutative 96.0%

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

      2. mul-1-neg 96.0%

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

      3. unsub-neg 96.0%

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

      4. associate-/l* 99.0%

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

      5. *-commutative 99.0%

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

   8. Simplified 99.0%

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

   9. Taylor expanded in x around 0 67.4%

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

       1. associate-*r/ 74.0%

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

   11. Simplified 74.0%

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

   if -4.6999999999999999e83 < y < 9.999999999999999e201

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+83} \lor \neg \left(y \leq 10^{+202}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 98.5%

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

Alternative 9: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

3. Taylor expanded in y around 0 91.8%

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

   1. mul-1-neg 91.8%

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

   2. associate-/l* 93.7%

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

   3. distribute-lft-neg-out 93.7%

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

   4. associate-*r/ 94.2%

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

   5. distribute-rgt-in 98.5%

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

   6. +-commutative 98.5%

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

   7. sub-neg 98.5%

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

   8. associate-*l/ 93.8%

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

   9. associate-/l* 94.0%

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

5. Simplified 94.0%

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

Alternative 10: 38.0% 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 98.5%

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

3. Taylor expanded in z around 0 39.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))

  (+ x (* (- y x) (/ z t))))