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

Percentage Accurate: 97.7% → 98.4%

Time: 6.6s

Alternatives: 8

Speedup: 0.5×

• 25.9% 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: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < -inf.0

   1. Initial program 90.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 99.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 99.1

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

   4. Applied rewrites 99.1%

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

4. Final simplification 99.3%

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

Alternative 2: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000000 \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5000000000.0) (not (<= (/ z t) 4e-20)))
   (* (/ z t) (- y x))
   (fma z (/ y t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5000000000.0) || !((z / t) <= 4e-20)) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = fma(z, (y / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5000000000.0) || !(Float64(z / t) <= 4e-20))
		tmp = Float64(Float64(z / t) * Float64(y - x));
	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], -5000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-20]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5e9 or 3.99999999999999978e-20 < (/.f64 z t)

   1. Initial program 95.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   7. Applied rewrites 95.6%

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

   if -5e9 < (/.f64 z t) < 3.99999999999999978e-20

   1. Initial program 99.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. frac-times N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-lft-neg-in N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-+.f64 53.3

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

   4. Applied rewrites 53.3%

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

   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 95.5

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

   7. Applied rewrites 95.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000000 \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-6} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e-6) (not (<= (/ z t) 4e-20))) (* (/ z t) y) (* 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-6) || !((z / t) <= 4e-20)) {
		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-6)) .or. (.not. ((z / t) <= 4d-20))) 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-6) || !((z / t) <= 4e-20)) {
		tmp = (z / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e-6) or not ((z / t) <= 4e-20):
		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-6) || !(Float64(z / t) <= 4e-20))
		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-6) || ~(((z / t) <= 4e-20)))
		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-6], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-20]], $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) < -1.99999999999999991e-6 or 3.99999999999999978e-20 < (/.f64 z t)

   1. Initial program 95.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 95.6

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

   4. Applied rewrites 95.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 62.4

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

   7. Applied rewrites 62.4%

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

   if -1.99999999999999991e-6 < (/.f64 z t) < 3.99999999999999978e-20

   1. Initial program 99.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
   6. 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. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 82.4

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

   7. Applied rewrites 82.4%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 82.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-6} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-6} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e-6) (not (<= (/ z t) 4e-20))) (* (/ y t) z) (* 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-6) || !((z / t) <= 4e-20)) {
		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-6)) .or. (.not. ((z / t) <= 4d-20))) 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-6) || !((z / t) <= 4e-20)) {
		tmp = (y / t) * z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e-6) or not ((z / t) <= 4e-20):
		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-6) || !(Float64(z / t) <= 4e-20))
		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-6) || ~(((z / t) <= 4e-20)))
		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-6], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-20]], $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) < -1.99999999999999991e-6 or 3.99999999999999978e-20 < (/.f64 z t)

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 55.4

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

   5. Applied rewrites 55.4%

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

   7. Applied rewrites 57.6%

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

   if -1.99999999999999991e-6 < (/.f64 z t) < 3.99999999999999978e-20

   1. Initial program 99.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
   6. 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. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 82.4

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

   7. Applied rewrites 82.4%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 82.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-6} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+57} \lor \neg \left(x \leq 15500000000000\right):\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e+57) (not (<= x 15500000000000.0)))
   (* (- 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 <= -5.5e+57) || !(x <= 15500000000000.0)) {
		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 <= -5.5e+57) || !(x <= 15500000000000.0))
		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, -5.5e+57], N[Not[LessEqual[x, 15500000000000.0]], $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 < -5.5000000000000002e57 or 1.55e13 < x

   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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 90.1

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

   5. Applied rewrites 90.1%

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

   if -5.5000000000000002e57 < x < 1.55e13

   1. Initial program 95.2%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. frac-times N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-lft-neg-in N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-+.f64 68.2

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

   4. Applied rewrites 68.2%

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

   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 85.2

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

   7. Applied rewrites 85.2%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+57} \lor \neg \left(x \leq 15500000000000\right):\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-140} \lor \neg \left(t \leq -1.45 \cdot 10^{-259}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.3e-140) (not (<= t -1.45e-259)))
   (fma z (/ y t) x)
   (/ (* (- x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.3e-140) || !(t <= -1.45e-259)) {
		tmp = fma(z, (y / t), x);
	} else {
		tmp = (-x * z) / t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.3e-140) || !(t <= -1.45e-259))
		tmp = fma(z, Float64(y / t), x);
	else
		tmp = Float64(Float64(Float64(-x) * z) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.3e-140], N[Not[LessEqual[t, -1.45e-259]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision] + x), $MachinePrecision], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2999999999999999e-140 or -1.45000000000000004e-259 < t

   1. Initial program 97.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. frac-times N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-lft-neg-in N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-+.f64 59.7

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

   4. Applied rewrites 59.7%

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

   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 79.1

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

   7. Applied rewrites 79.1%

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

   if -1.2999999999999999e-140 < t < -1.45000000000000004e-259

   1. Initial program 94.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 94.5

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

   5. Applied rewrites 94.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 79.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-140} \lor \neg \left(t \leq -1.45 \cdot 10^{-259}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. lift-/.f64 N/A

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

   6. lift--.f64 N/A

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

   7. flip-- N/A

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

   8. frac-times N/A

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

   9. associate-/l* N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. sub-neg N/A

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

   13. +-commutative N/A

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

   14. distribute-lft-neg-in N/A

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

   15. lower-fma.f64 N/A

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

   16. lower-neg.f64 N/A

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

   17. lower-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lower-*.f64 N/A

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

   20. lower-+.f64 60.9

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

4. Applied rewrites 60.9%

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

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 75.9

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

7. Applied rewrites 75.9%

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

Alternative 8: 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 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. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
6. 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. mul-1-neg N/A

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

   4. sub-neg N/A

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 65.7

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

7. Applied rewrites 65.7%

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

8. Taylor expanded in z around 0

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

10. Applied rewrites 40.9%

    \[\leadsto 1 \cdot x \]
11. Add Preprocessing

Developer Target 1: 97.5% 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 2024324 
(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))))