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

Percentage Accurate: 97.6% → 98.0%

Time: 6.0s

Alternatives: 12

Speedup: 0.9×

• 25.0% 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: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2e-16) (fma (/ z t) (- y x) x) (fma z (/ (- y x) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2e-16) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = fma(z, ((y - x) / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2e-16)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = fma(z, Float64(Float64(y - x) / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2e-16], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2e-16

   1. Initial program 98.2%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lower-fma.f64 98.2

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

   4. Applied rewrites 98.2%

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

   if 2e-16 < z

   1. Initial program 90.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 100.0

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

   4. Applied rewrites 100.0%

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

Alternative 2: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000000000 \lor \neg \left(\frac{z}{t} \leq 0.01\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -500000000000.0) (not (<= (/ z t) 0.01)))
   (* (/ z t) (- y x))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500000000000.0) || !((z / t) <= 0.01)) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-500000000000.0d0)) .or. (.not. ((z / t) <= 0.01d0))) then
        tmp = (z / t) * (y - x)
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -500000000000.0) || !((z / t) <= 0.01)) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -500000000000.0) or not ((z / t) <= 0.01):
		tmp = (z / t) * (y - x)
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -500000000000.0) || !(Float64(z / t) <= 0.01))
		tmp = Float64(Float64(z / t) * Float64(y - x));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -500000000000.0) || ~(((z / t) <= 0.01)))
		tmp = (z / t) * (y - x);
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -500000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.01]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5e11 or 0.0100000000000000002 < (/.f64 z t)

   1. Initial program 95.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 92.2

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

   5. Applied rewrites 92.2%

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

   7. Applied rewrites 94.2%

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

   if -5e11 < (/.f64 z t) < 0.0100000000000000002

   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

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 97.2

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

   7. Applied rewrites 97.2%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000000000 \lor \neg \left(\frac{z}{t} \leq 0.01\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-126} \lor \neg \left(\frac{z}{t} \leq 20\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e-126) (not (<= (/ z t) 20.0)))
   (* (/ z t) (- y x))
   (* (- 1.0 (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-126) || !((z / t) <= 20.0)) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = (1.0 - (z / t)) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-2d-126)) .or. (.not. ((z / t) <= 20.0d0))) then
        tmp = (z / t) * (y - x)
    else
        tmp = (1.0d0 - (z / t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e-126) || !((z / t) <= 20.0)) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = (1.0 - (z / t)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e-126) or not ((z / t) <= 20.0):
		tmp = (z / t) * (y - x)
	else:
		tmp = (1.0 - (z / t)) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2e-126) || !(Float64(z / t) <= 20.0))
		tmp = Float64(Float64(z / t) * Float64(y - x));
	else
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2e-126) || ~(((z / t) <= 20.0)))
		tmp = (z / t) * (y - x);
	else
		tmp = (1.0 - (z / t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2e-126], N[Not[LessEqual[N[(z / t), $MachinePrecision], 20.0]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.9999999999999999e-126 or 20 < (/.f64 z t)

   1. Initial program 95.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 86.0

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

   5. Applied rewrites 86.0%

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

   7. Applied rewrites 90.3%

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

   if -1.9999999999999999e-126 < (/.f64 z t) < 20

   1. Initial program 97.7%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 83.6

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

   5. Applied rewrites 83.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-126} \lor \neg \left(\frac{z}{t} \leq 20\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 20000000000000:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e-126)
   (* (/ z t) (- y x))
   (if (<= (/ z t) 20000000000000.0)
     (* (- 1.0 (/ z t)) x)
     (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-126) {
		tmp = (z / t) * (y - x);
	} else if ((z / t) <= 20000000000000.0) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d-126)) then
        tmp = (z / t) * (y - x)
    else if ((z / t) <= 20000000000000.0d0) then
        tmp = (1.0d0 - (z / t)) * x
    else
        tmp = ((y - x) * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-126) {
		tmp = (z / t) * (y - x);
	} else if ((z / t) <= 20000000000000.0) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e-126:
		tmp = (z / t) * (y - x)
	elif (z / t) <= 20000000000000.0:
		tmp = (1.0 - (z / t)) * x
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-126)
		tmp = Float64(Float64(z / t) * Float64(y - x));
	elseif (Float64(z / t) <= 20000000000000.0)
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e-126)
		tmp = (z / t) * (y - x);
	elseif ((z / t) <= 20000000000000.0)
		tmp = (1.0 - (z / t)) * x;
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e-126], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 20000000000000.0], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.9999999999999999e-126

   1. Initial program 97.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 82.3

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

   5. Applied rewrites 82.3%

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

   7. Applied rewrites 87.9%

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

   if -1.9999999999999999e-126 < (/.f64 z t) < 2e13

   1. Initial program 97.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 82.5

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

   5. Applied rewrites 82.5%

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

   if 2e13 < (/.f64 z t)

   1. Initial program 93.5%

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

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

   5. Applied rewrites 92.1%

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

   7. Applied rewrites 96.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 20000000000000:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-241} \lor \neg \left(z \leq 3.4 \cdot 10^{-76}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-241) (not (<= z 3.4e-76)))
   (fma z (/ (- y x) t) x)
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-241) || !(z <= 3.4e-76)) {
		tmp = fma(z, ((y - x) / t), x);
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-241) || !(z <= 3.4e-76))
		tmp = fma(z, Float64(Float64(y - x) / t), x);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-241], N[Not[LessEqual[z, 3.4e-76]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e-241 or 3.3999999999999999e-76 < z

   1. Initial program 96.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. 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 96.4

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

   4. Applied rewrites 96.4%

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

   if -1.6499999999999999e-241 < z < 3.3999999999999999e-76

   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

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 95.4

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

   7. Applied rewrites 95.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-241} \lor \neg \left(z \leq 3.4 \cdot 10^{-76}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+41} \lor \neg \left(y \leq 2.25 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e+41) (not (<= y 2.25e+27)))
   (* (/ z t) y)
   (* (- 1.0 (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e+41) || !(y <= 2.25e+27)) {
		tmp = (z / t) * y;
	} else {
		tmp = (1.0 - (z / t)) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.6d+41)) .or. (.not. (y <= 2.25d+27))) then
        tmp = (z / t) * y
    else
        tmp = (1.0d0 - (z / t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e+41) || !(y <= 2.25e+27)) {
		tmp = (z / t) * y;
	} else {
		tmp = (1.0 - (z / t)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e+41) or not (y <= 2.25e+27):
		tmp = (z / t) * y
	else:
		tmp = (1.0 - (z / t)) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e+41) || !(y <= 2.25e+27))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.6e+41) || ~((y <= 2.25e+27)))
		tmp = (z / t) * y;
	else
		tmp = (1.0 - (z / t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e+41], N[Not[LessEqual[y, 2.25e+27]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999997e41 or 2.25e27 < y

   1. Initial program 97.7%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 97.7

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

   4. Applied rewrites 97.7%

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

   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 67.8

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

   7. Applied rewrites 67.8%

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

   if -4.5999999999999997e41 < y < 2.25e27

   1. Initial program 95.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 83.4

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

   5. Applied rewrites 83.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+41} \lor \neg \left(y \leq 2.25 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-5} \lor \neg \left(y \leq 15500000000000\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-5) (not (<= y 15500000000000.0)))
   (* (/ z t) y)
   (/ (* (- x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0)) {
		tmp = (z / t) * y;
	} else {
		tmp = (-x * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.3d-5)) .or. (.not. (y <= 15500000000000.0d0))) then
        tmp = (z / t) * y
    else
        tmp = (-x * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0)) {
		tmp = (z / t) * y;
	} else {
		tmp = (-x * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.3e-5) or not (y <= 15500000000000.0):
		tmp = (z / t) * y
	else:
		tmp = (-x * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(Float64(Float64(-x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.3e-5) || ~((y <= 15500000000000.0)))
		tmp = (z / t) * y;
	else
		tmp = (-x * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e-5], N[Not[LessEqual[y, 15500000000000.0]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3000000000000002e-5 or 1.55e13 < y

   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. lower-fma.f64 98.0

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

   4. Applied rewrites 98.0%

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

   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 63.3

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

   7. Applied rewrites 63.3%

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

   if -4.3000000000000002e-5 < y < 1.55e13

   1. Initial program 95.2%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 46.8

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.9%

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

   10. Applied rewrites 38.4%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-5} \lor \neg \left(y \leq 15500000000000\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-5} \lor \neg \left(y \leq 15500000000000\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-5) (not (<= y 15500000000000.0)))
   (* (/ z t) y)
   (* (/ (- x) t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0)) {
		tmp = (z / t) * y;
	} else {
		tmp = (-x / t) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.3d-5)) .or. (.not. (y <= 15500000000000.0d0))) then
        tmp = (z / t) * y
    else
        tmp = (-x / t) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0)) {
		tmp = (z / t) * y;
	} else {
		tmp = (-x / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.3e-5) or not (y <= 15500000000000.0):
		tmp = (z / t) * y
	else:
		tmp = (-x / t) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(Float64(Float64(-x) / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.3e-5) || ~((y <= 15500000000000.0)))
		tmp = (z / t) * y;
	else
		tmp = (-x / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e-5], N[Not[LessEqual[y, 15500000000000.0]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3000000000000002e-5 or 1.55e13 < y

   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. lower-fma.f64 98.0

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

   4. Applied rewrites 98.0%

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

   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 63.3

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

   7. Applied rewrites 63.3%

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

   if -4.3000000000000002e-5 < y < 1.55e13

   1. Initial program 95.2%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 46.8

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-5} \lor \neg \left(y \leq 15500000000000\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-5} \lor \neg \left(y \leq 15500000000000\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-5) (not (<= y 15500000000000.0)))
   (* (/ z t) y)
   (* (- x) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0)) {
		tmp = (z / t) * y;
	} else {
		tmp = -x * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.3d-5)) .or. (.not. (y <= 15500000000000.0d0))) then
        tmp = (z / t) * y
    else
        tmp = -x * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0)) {
		tmp = (z / t) * y;
	} else {
		tmp = -x * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.3e-5) or not (y <= 15500000000000.0):
		tmp = (z / t) * y
	else:
		tmp = -x * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e-5) || !(y <= 15500000000000.0))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(Float64(-x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.3e-5) || ~((y <= 15500000000000.0)))
		tmp = (z / t) * y;
	else
		tmp = -x * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e-5], N[Not[LessEqual[y, 15500000000000.0]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[((-x) * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3000000000000002e-5 or 1.55e13 < y

   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. lower-fma.f64 98.0

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

   4. Applied rewrites 98.0%

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

   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 63.3

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

   7. Applied rewrites 63.3%

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

   if -4.3000000000000002e-5 < y < 1.55e13

   1. Initial program 95.2%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 46.8

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.9%

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

   10. Applied rewrites 36.5%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-5} \lor \neg \left(y \leq 15500000000000\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 = (z / t) * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]
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 96.7

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

4. Applied rewrites 96.7%

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

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 41.4

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

7. Applied rewrites 41.4%

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

Alternative 11: 38.0% accurate, 1.4× speedup

Math

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

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(Float64(y * z) / t)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]
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 38.2

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

5. Applied rewrites 38.2%

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

7. Applied rewrites 39.6%

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

8. Final simplification 39.6%

   \[\leadsto \frac{y \cdot z}{t} \]
9. Add Preprocessing

Alternative 12: 38.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 / t) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]
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 38.2

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

5. Applied rewrites 38.2%

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

6. Final simplification 38.2%

   \[\leadsto \frac{y}{t} \cdot z \]
7. 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 2024326 
(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))))