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

Percentage Accurate: 97.6% → 97.6%

Time: 6.1s

Alternatives: 10

Speedup: 1.1×

• 25.3% 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: 97.6% 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: 97.6% 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 98.1%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]
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 98.1

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

4. Applied rewrites 98.1%

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

Alternative 2: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000 \lor \neg \left(\frac{z}{t} \leq 10^{-13}\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2000.0) (not (<= (/ z t) 1e-13)))
   (/ (* (- y x) z) t)
   (fma z (/ y t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2000.0) || !((z / t) <= 1e-13)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = fma(z, (y / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2000.0) || !(Float64(z / t) <= 1e-13))
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = fma(z, Float64(y / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-13]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e3 or 1e-13 < (/.f64 z t)

   1. Initial program 96.7%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 89.0

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

   5. Applied rewrites 89.0%

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

   7. Applied rewrites 93.4%

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

   if -2e3 < (/.f64 z t) < 1e-13

   1. Initial program 99.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 95.5

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

   4. Applied rewrites 95.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 97.6

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

   7. Applied rewrites 97.6%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000 \lor \neg \left(\frac{z}{t} \leq 10^{-13}\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000 \lor \neg \left(\frac{z}{t} \leq 1\right):\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2000.0) (not (<= (/ z t) 1.0)))
   (* (/ (- y x) t) z)
   (fma z (/ y t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2000.0) || !((z / t) <= 1.0)) {
		tmp = ((y - x) / t) * z;
	} else {
		tmp = fma(z, (y / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2000.0) || !(Float64(z / t) <= 1.0))
		tmp = Float64(Float64(Float64(y - x) / t) * z);
	else
		tmp = fma(z, Float64(y / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e3 or 1 < (/.f64 z t)

   1. Initial program 96.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 90.3

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

   5. Applied rewrites 90.3%

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

   if -2e3 < (/.f64 z t) < 1

   1. Initial program 99.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 94.2

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

   4. Applied rewrites 94.2%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 96.3

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

   7. Applied rewrites 96.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000 \lor \neg \left(\frac{z}{t} \leq 1\right):\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+65}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 2e+15)
   (fma z (/ y t) x)
   (if (<= (/ z t) 2e+65) (* (/ (- z) t) x) (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 2e+15) {
		tmp = fma(z, (y / t), x);
	} else if ((z / t) <= 2e+65) {
		tmp = (-z / t) * x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 2e+15)
		tmp = fma(z, Float64(y / t), x);
	elseif (Float64(z / t) <= 2e+65)
		tmp = Float64(Float64(Float64(-z) / t) * x);
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 2e+15], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e+65], N[(N[((-z) / t), $MachinePrecision] * x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < 2e15

   1. Initial program 98.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 94.1

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 84.3

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

   7. Applied rewrites 84.3%

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

   if 2e15 < (/.f64 z t) < 2e65

   1. Initial program 99.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 86.3

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

   5. Applied rewrites 86.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 86.3%

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

   if 2e65 < (/.f64 z t)

   1. Initial program 98.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 61.8

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

   5. Applied rewrites 61.8%

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

   7. Applied rewrites 63.7%

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

Alternative 5: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e-25) (not (<= (/ z t) 2e-27)))
   (* (/ z t) y)
   (* 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-25) || !((z / t) <= 2e-27)) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * 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-25)) .or. (.not. ((z / t) <= 2d-27))) then
        tmp = (z / t) * y
    else
        tmp = 1.0d0 * 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-25) || !((z / t) <= 2e-27)) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e-25) or not ((z / t) <= 2e-27):
		tmp = (z / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2e-25) || !(Float64(z / t) <= 2e-27))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2e-25) || ~(((z / t) <= 2e-27)))
		tmp = (z / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2e-25], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-27]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.00000000000000008e-25 or 2.0000000000000001e-27 < (/.f64 z t)

   1. Initial program 96.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 54.3

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

   5. Applied rewrites 54.3%

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

   7. Applied rewrites 57.7%

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

   if -2.00000000000000008e-25 < (/.f64 z t) < 2.0000000000000001e-27

   1. Initial program 99.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 75.4

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 75.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e-25) (not (<= (/ z t) 2e-27)))
   (* (/ y t) z)
   (* 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-25) || !((z / t) <= 2e-27)) {
		tmp = (y / t) * z;
	} else {
		tmp = 1.0 * 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-25)) .or. (.not. ((z / t) <= 2d-27))) then
        tmp = (y / t) * z
    else
        tmp = 1.0d0 * 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-25) || !((z / t) <= 2e-27)) {
		tmp = (y / t) * z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e-25) or not ((z / t) <= 2e-27):
		tmp = (y / t) * z
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2e-25) || !(Float64(z / t) <= 2e-27))
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2e-25) || ~(((z / t) <= 2e-27)))
		tmp = (y / t) * z;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2e-25], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-27]], $MachinePrecision]], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.00000000000000008e-25 or 2.0000000000000001e-27 < (/.f64 z t)

   1. Initial program 96.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 54.3

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

   5. Applied rewrites 54.3%

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

   if -2.00000000000000008e-25 < (/.f64 z t) < 2.0000000000000001e-27

   1. Initial program 99.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 75.4

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 75.4%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 5e-8) (fma z (/ y t) x) (* (/ z t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 5e-8) {
		tmp = fma(z, (y / t), x);
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 5e-8)
		tmp = fma(z, Float64(y / t), x);
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 5e-8], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < 4.9999999999999998e-8

   1. Initial program 98.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 95.5

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

   4. Applied rewrites 95.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 85.9

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

   7. Applied rewrites 85.9%

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

   if 4.9999999999999998e-8 < (/.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 50.1

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

   5. Applied rewrites 50.1%

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

   7. Applied rewrites 55.7%

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

Alternative 8: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21000000000000 \lor \neg \left(x \leq 4 \cdot 10^{+71}\right):\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -21000000000000.0) (not (<= x 4e+71)))
   (* (- 1.0 (/ z t)) x)
   (fma z (/ y t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -21000000000000.0) || !(x <= 4e+71)) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = fma(z, (y / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -21000000000000.0) || !(x <= 4e+71))
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = fma(z, Float64(y / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -21000000000000.0], N[Not[LessEqual[x, 4e+71]], $MachinePrecision]], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e13 or 4.0000000000000002e71 < x

   1. Initial program 99.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 92.1

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

   5. Applied rewrites 92.1%

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

   if -2.1e13 < x < 4.0000000000000002e71

   1. Initial program 97.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 94.7

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 85.1

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

   7. Applied rewrites 85.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000000 \lor \neg \left(x \leq 4 \cdot 10^{+71}\right):\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+121}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e+121) (* (- 1.0 (/ z t)) x) (fma z (/ (- y x) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e+121) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = fma(z, ((y - x) / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e+121)
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = fma(z, Float64(Float64(y - x) / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e+121], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e121

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   if -2.5999999999999999e121 < x

   1. Initial program 97.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. 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 94.4

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

   4. Applied rewrites 94.4%

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

Alternative 10: 38.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Python

def code(x, y, z, t):
	return 1.0 * x

Julia

function code(x, y, z, t)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 98.1%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]
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 63.2

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

5. Applied rewrites 63.2%

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

6. Taylor expanded in z around 0

   \[\leadsto 1 \cdot x \]
7. Step-by-step derivation

8. Applied rewrites 38.5%

   \[\leadsto 1 \cdot x \]
9. 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 2024320 
(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))))