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

Percentage Accurate: 97.7% → 97.7%

Time: 5.7s

Alternatives: 9

Speedup: 1.1×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 98.3

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

4. Applied rewrites 98.3%

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

Alternative 2: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-33} \lor \neg \left(\frac{z}{t} \leq 50000\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e-33) (not (<= (/ z t) 50000.0)))
   (/ (* (- y x) z) t)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e-33) || !((z / t) <= 50000.0)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -4e-33) || !(Float64(z / t) <= 50000.0))
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -4e-33], N[Not[LessEqual[N[(z / t), $MachinePrecision], 50000.0]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.0000000000000002e-33 or 5e4 < (/.f64 z t)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 89.4

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

   5. Applied rewrites 89.4%

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

   7. Applied rewrites 92.4%

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

   if -4.0000000000000002e-33 < (/.f64 z t) < 5e4

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-fma.f64 94.4

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

   6. Applied rewrites 94.4%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 95.5

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

   9. Applied rewrites 95.5%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-33} \lor \neg \left(\frac{z}{t} \leq 50000\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000 \lor \neg \left(\frac{z}{t} \leq 0.0005\right):\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1000000.0) (not (<= (/ z t) 0.0005)))
   (* (/ (- y x) t) z)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000000.0) || !((z / t) <= 0.0005)) {
		tmp = ((y - x) / t) * z;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1000000.0) || !(Float64(z / t) <= 0.0005))
		tmp = Float64(Float64(Float64(y - x) / t) * z);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.0005]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e6 or 5.0000000000000001e-4 < (/.f64 z t)

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 92.6

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

   5. Applied rewrites 92.6%

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

   if -1e6 < (/.f64 z t) < 5.0000000000000001e-4

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-fma.f64 92.4

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

   6. Applied rewrites 92.4%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 92.9

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

   9. Applied rewrites 92.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000 \lor \neg \left(\frac{z}{t} \leq 0.0005\right):\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 200000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+236}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 200000000.0)
   (fma (/ y t) z x)
   (if (<= (/ z t) 1e+236) (/ (* (- x) z) t) (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 200000000.0) {
		tmp = fma((y / t), z, x);
	} else if ((z / t) <= 1e+236) {
		tmp = (-x * z) / t;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 200000000.0)
		tmp = fma(Float64(y / t), z, x);
	elseif (Float64(z / t) <= 1e+236)
		tmp = Float64(Float64(Float64(-x) * z) / t);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 200000000.0], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+236], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < 2e8

   1. Initial program 98.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.3

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

   4. Applied rewrites 98.3%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-fma.f64 92.7

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

   6. Applied rewrites 92.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 82.9

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

   9. Applied rewrites 82.9%

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

   if 2e8 < (/.f64 z t) < 1.00000000000000005e236

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

   7. Applied rewrites 91.8%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 65.0%

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

   if 1.00000000000000005e236 < (/.f64 z t)

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 70.5

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

   5. Applied rewrites 70.5%

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

   7. Applied rewrites 78.9%

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

Alternative 5: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 200000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+236}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 200000000.0)
   (fma (/ y t) z x)
   (if (<= (/ z t) 1e+236) (* (/ (- x) t) z) (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 200000000.0) {
		tmp = fma((y / t), z, x);
	} else if ((z / t) <= 1e+236) {
		tmp = (-x / t) * z;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 200000000.0)
		tmp = fma(Float64(y / t), z, x);
	elseif (Float64(z / t) <= 1e+236)
		tmp = Float64(Float64(Float64(-x) / t) * z);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 200000000.0], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+236], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < 2e8

   1. Initial program 98.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.3

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

   4. Applied rewrites 98.3%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-fma.f64 92.7

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

   6. Applied rewrites 92.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 82.9

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

   9. Applied rewrites 82.9%

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

   if 2e8 < (/.f64 z t) < 1.00000000000000005e236

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 57.4%

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

   if 1.00000000000000005e236 < (/.f64 z t)

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 70.5

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

   5. Applied rewrites 70.5%

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

   7. Applied rewrites 78.9%

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

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 50000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 50000.0) (fma (/ y t) z x) (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 50000.0) {
		tmp = fma((y / t), z, x);
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 50000.0)
		tmp = fma(Float64(y / t), z, x);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 50000.0], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < 5e4

   1. Initial program 98.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.3

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

   4. Applied rewrites 98.3%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-fma.f64 92.7

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

   6. Applied rewrites 92.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 83.2

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

   9. Applied rewrites 83.2%

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

   if 5e4 < (/.f64 z t)

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 50.2

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

   5. Applied rewrites 50.2%

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

   7. Applied rewrites 55.6%

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

Alternative 7: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-60} \lor \neg \left(x \leq 6.8 \cdot 10^{+34}\right):\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e-60) (not (<= x 6.8e+34)))
   (* (- 1.0 (/ z t)) x)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-60) || !(x <= 6.8e+34)) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e-60) || !(x <= 6.8e+34))
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e-60], N[Not[LessEqual[x, 6.8e+34]], $MachinePrecision]], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999958e-60 or 6.7999999999999999e34 < x

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -9.49999999999999958e-60 < x < 6.7999999999999999e34

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 97.4

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

   4. Applied rewrites 97.4%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-fma.f64 94.2

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

   6. Applied rewrites 94.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 89.4

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

   9. Applied rewrites 89.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-60} \lor \neg \left(x \leq 6.8 \cdot 10^{+34}\right):\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-/.f64 N/A

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

   6. associate-*l/ N/A

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

   7. associate-/l* N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 92.8

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

4. Applied rewrites 92.8%

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

Alternative 9: 41.5% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around 0

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 42.2

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

5. Applied rewrites 42.2%

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

7. Applied rewrites 45.8%

   \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]
8. Add Preprocessing

Developer Target 1: 97.6% 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 2024329 
(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))))