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

Percentage Accurate: 97.8% → 97.8%

Time: 6.8s

Alternatives: 11

Speedup: 1.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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. Add Preprocessing

Alternative 2: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-7}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -200000000000.0)
     t_1
     (if (<= (/ z t) 1e-7) (+ (/ (* y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 1e-7) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    if ((z / t) <= (-200000000000.0d0)) then
        tmp = t_1
    else if ((z / t) <= 1d-7) then
        tmp = ((y * z) / t) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 1e-7) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if (z / t) <= -200000000000.0:
		tmp = t_1
	elif (z / t) <= 1e-7:
		tmp = ((y * z) / t) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -200000000000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-7)
		tmp = Float64(Float64(Float64(y * z) / t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if ((z / t) <= -200000000000.0)
		tmp = t_1;
	elseif ((z / t) <= 1e-7)
		tmp = ((y * z) / t) + x;
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(z / t), $MachinePrecision], -200000000000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-7], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e11 or 9.9999999999999995e-8 < (/.f64 z t)

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   7. Applied rewrites 95.6%

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

   if -2e11 < (/.f64 z t) < 9.9999999999999995e-8

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 96.2

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

   5. Applied rewrites 96.2%

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

   7. Applied rewrites 97.6%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-7}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-7}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -200000000000.0)
     t_1
     (if (<= (/ z t) 1e-7) (+ (* (/ y t) z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 1e-7) {
		tmp = ((y / t) * z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    if ((z / t) <= (-200000000000.0d0)) then
        tmp = t_1
    else if ((z / t) <= 1d-7) then
        tmp = ((y / t) * z) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 1e-7) {
		tmp = ((y / t) * z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if (z / t) <= -200000000000.0:
		tmp = t_1
	elif (z / t) <= 1e-7:
		tmp = ((y / t) * z) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -200000000000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-7)
		tmp = Float64(Float64(Float64(y / t) * z) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if ((z / t) <= -200000000000.0)
		tmp = t_1;
	elseif ((z / t) <= 1e-7)
		tmp = ((y / t) * z) + x;
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(z / t), $MachinePrecision], -200000000000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-7], N[(N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e11 or 9.9999999999999995e-8 < (/.f64 z t)

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   7. Applied rewrites 95.6%

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

   if -2e11 < (/.f64 z t) < 9.9999999999999995e-8

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 96.2

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

   5. Applied rewrites 96.2%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-7}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e+28)
   (/ (* (- y x) z) t)
   (if (<= (/ z t) 1e-24) (- x (* (/ x t) z)) (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e+28) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 1e-24) {
		tmp = x - ((x / t) * z);
	} 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) <= (-1d+28)) then
        tmp = ((y - x) * z) / t
    else if ((z / t) <= 1d-24) then
        tmp = x - ((x / t) * z)
    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) <= -1e+28) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 1e-24) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e+28:
		tmp = ((y - x) * z) / t
	elif (z / t) <= 1e-24:
		tmp = x - ((x / t) * z)
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e+28)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e+28)
		tmp = ((y - x) * z) / t;
	elseif ((z / t) <= 1e-24)
		tmp = x - ((x / t) * z);
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e+28], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -9.99999999999999958e27

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 96.4

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

   5. Applied rewrites 96.4%

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

   if -9.99999999999999958e27 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if 9.99999999999999924e-25 < (/.f64 z t)

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 90.1

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

   5. Applied rewrites 90.1%

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

   7. Applied rewrites 95.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -1e+28)
     t_1
     (if (<= (/ z t) 1e-24) (- x (* (/ x t) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -1e+28) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    if ((z / t) <= (-1d+28)) then
        tmp = t_1
    else if ((z / t) <= 1d-24) then
        tmp = x - ((x / t) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -1e+28) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if (z / t) <= -1e+28:
		tmp = t_1
	elif (z / t) <= 1e-24:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+28)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+28)
		tmp = t_1;
	elseif ((z / t) <= 1e-24)
		tmp = x - ((x / t) * z);
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+28], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -9.99999999999999958e27 or 9.99999999999999924e-25 < (/.f64 z t)

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   7. Applied rewrites 95.1%

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

   if -9.99999999999999958e27 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.2

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

   5. Applied rewrites 78.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -1e-59) t_1 (if (<= (/ z t) 1e-24) (/ (* x t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    if ((z / t) <= (-1d-59)) then
        tmp = t_1
    else if ((z / t) <= 1d-24) then
        tmp = (x * t) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if (z / t) <= -1e-59:
		tmp = t_1
	elif (z / t) <= 1e-24:
		tmp = (x * t) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e-59)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e-59)
		tmp = t_1;
	elseif ((z / t) <= 1e-24)
		tmp = (x * t) / t;
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e-59], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e-59 or 9.99999999999999924e-25 < (/.f64 z t)

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 88.4

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 92.1%

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

   if -1e-59 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 60.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-59}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -200000000000.0)
   (* (/ (- x) t) z)
   (if (<= (/ z t) 1e-24) (/ (* x t) t) (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = (-x / t) * z;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-200000000000.0d0)) then
        tmp = (-x / t) * z
    else if ((z / t) <= 1d-24) then
        tmp = (x * t) / t
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -200000000000.0) {
		tmp = (-x / t) * z;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -200000000000.0:
		tmp = (-x / t) * z
	elif (z / t) <= 1e-24:
		tmp = (x * t) / t
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -200000000000.0)
		tmp = Float64(Float64(Float64(-x) / t) * z);
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -200000000000.0)
		tmp = (-x / t) * z;
	elseif ((z / t) <= 1e-24)
		tmp = (x * t) / t;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -200000000000.0], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.4%

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

   if -2e11 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 79.3

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 58.3%

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

   if 9.99999999999999924e-25 < (/.f64 z t)

   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%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   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 59.2

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

   7. Applied rewrites 59.2%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000000000:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -1e-59) t_1 (if (<= (/ z t) 1e-24) (/ (* x t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-1d-59)) then
        tmp = t_1
    else if ((z / t) <= 1d-24) then
        tmp = (x * t) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -1e-59:
		tmp = t_1
	elif (z / t) <= 1e-24:
		tmp = (x * t) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e-59)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e-59)
		tmp = t_1;
	elseif ((z / t) <= 1e-24)
		tmp = (x * t) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e-59], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e-59 or 9.99999999999999924e-25 < (/.f64 z t)

   1. Initial program 97.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   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 53.2

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

   7. Applied rewrites 53.2%

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

   if -1e-59 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 60.6%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e-59)
   (* (/ y t) z)
   (if (<= (/ z t) 1e-24) (/ (* x t) t) (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = (y / t) * z;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1d-59)) then
        tmp = (y / t) * z
    else if ((z / t) <= 1d-24) then
        tmp = (x * t) / t
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = (y / t) * z;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e-59:
		tmp = (y / t) * z
	elif (z / t) <= 1e-24:
		tmp = (x * t) / t
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e-59)
		tmp = Float64(Float64(y / t) * z);
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e-59)
		tmp = (y / t) * z;
	elseif ((z / t) <= 1e-24)
		tmp = (x * t) / t;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e-59], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e-59

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   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 44.6

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

   5. Applied rewrites 44.6%

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

   if -1e-59 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 60.6%

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

   if 9.99999999999999924e-25 < (/.f64 z t)

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   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 49.5

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

   5. Applied rewrites 49.5%

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

   7. Applied rewrites 53.8%

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

Alternative 10: 53.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot z\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y t) z)))
   (if (<= (/ z t) -1e-59) t_1 (if (<= (/ z t) 1e-24) (/ (* x t) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / t) * z
    if ((z / t) <= (-1d-59)) then
        tmp = t_1
    else if ((z / t) <= 1d-24) then
        tmp = (x * t) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if ((z / t) <= -1e-59) {
		tmp = t_1;
	} else if ((z / t) <= 1e-24) {
		tmp = (x * t) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) * z
	tmp = 0
	if (z / t) <= -1e-59:
		tmp = t_1
	elif (z / t) <= 1e-24:
		tmp = (x * t) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) * z)
	tmp = 0.0
	if (Float64(z / t) <= -1e-59)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-24)
		tmp = Float64(Float64(x * t) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) * z;
	tmp = 0.0;
	if ((z / t) <= -1e-59)
		tmp = t_1;
	elseif ((z / t) <= 1e-24)
		tmp = (x * t) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e-59], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-24], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e-59 or 9.99999999999999924e-25 < (/.f64 z t)

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   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 46.8

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

   5. Applied rewrites 46.8%

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

   if -1e-59 < (/.f64 z t) < 9.99999999999999924e-25

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 60.6%

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

Alternative 11: 37.9% 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 97.4%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
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 33.8

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

5. Applied rewrites 33.8%

   \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]
6. 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 2024276 
(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))))