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

Percentage Accurate: 97.5% → 98.3%

Time: 7.3s

Alternatives: 10

Speedup: 0.5×

• 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: 97.5% 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: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 10^{+172}:\\ \;\;\;\;x - \left(\frac{-1}{t} \cdot z\right) \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(x - y\right) \cdot z, \frac{-1}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 1e+172)
   (- x (* (* (/ -1.0 t) z) (- y x)))
   (fma (* (- x y) z) (/ -1.0 t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 1e+172) {
		tmp = x - (((-1.0 / t) * z) * (y - x));
	} else {
		tmp = fma(((x - y) * z), (-1.0 / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 1e+172)
		tmp = Float64(x - Float64(Float64(Float64(-1.0 / t) * z) * Float64(y - x)));
	else
		tmp = fma(Float64(Float64(x - y) * z), Float64(-1.0 / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 1e+172], N[(x - N[(N[(N[(-1.0 / t), $MachinePrecision] * z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] * z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < 1.0000000000000001e172

   1. Initial program 98.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. frac-2neg N/A

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

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. neg-mul-1 N/A

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

      7. associate-/r* N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-neg.f64 99.0

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

   4. Applied rewrites 99.0%

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

   if 1.0000000000000001e172 < (/.f64 z t)

   1. Initial program 78.2%

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

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

      5. associate-*r/ N/A

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

      6. frac-2neg N/A

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

      7. div-inv N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. associate-/r* N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 10^{+172}:\\ \;\;\;\;x - \left(\frac{-1}{t} \cdot z\right) \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(x - y\right) \cdot z, \frac{-1}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) z) t)))
   (if (<= (/ z t) -1000.0)
     t_1
     (if (<= (/ z t) 0.2) (+ (* (/ 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) <= -1000.0) {
		tmp = t_1;
	} else if ((z / t) <= 0.2) {
		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) <= (-1000.0d0)) then
        tmp = t_1
    else if ((z / t) <= 0.2d0) 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) <= -1000.0) {
		tmp = t_1;
	} else if ((z / t) <= 0.2) {
		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) <= -1000.0:
		tmp = t_1
	elif (z / t) <= 0.2:
		tmp = ((y / t) * z) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y - x) * z) / t)
	tmp = 0.0
	if (Float64(z / t) <= -1000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 0.2)
		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) <= -1000.0)
		tmp = t_1;
	elseif ((z / t) <= 0.2)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 0.2], 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) < -1e3 or 0.20000000000000001 < (/.f64 z t)

   1. Initial program 92.9%

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

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

   if -1e3 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 99.2%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 93.4

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

   5. Applied rewrites 93.4%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) z) t)))
   (if (<= (/ z t) -2e-43) t_1 (if (<= (/ z t) 0.2) (- 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) <= -2e-43) {
		tmp = t_1;
	} else if ((z / t) <= 0.2) {
		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) <= (-2d-43)) then
        tmp = t_1
    else if ((z / t) <= 0.2d0) 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) <= -2e-43) {
		tmp = t_1;
	} else if ((z / t) <= 0.2) {
		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) <= -2e-43:
		tmp = t_1
	elif (z / t) <= 0.2:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y - x) * z) / t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-43)
		tmp = t_1;
	elseif (Float64(z / t) <= 0.2)
		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) <= -2e-43)
		tmp = t_1;
	elseif ((z / t) <= 0.2)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e-43], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 0.2], 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) < -2.00000000000000015e-43 or 0.20000000000000001 < (/.f64 z t)

   1. Initial program 93.5%

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

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

   5. Applied rewrites 90.3%

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

   if -2.00000000000000015e-43 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 99.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 72.9

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

   5. Applied rewrites 72.9%

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

Alternative 4: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - \left(x - y\right) \cdot \frac{z}{t} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- x (* (- x y) (/ z t))) 2e+307)
   (fma (/ z t) (- y x) x)
   (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x - ((x - y) * (z / t))) <= 2e+307) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x - Float64(Float64(x - y) * Float64(z / t))) <= 2e+307)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x - N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+307], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 1.99999999999999997e307

   1. Initial program 98.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 98.9

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

   4. Applied rewrites 98.9%

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

   if 1.99999999999999997e307 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 79.5%

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

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

   5. Applied rewrites 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(x - y\right) \cdot \frac{z}{t} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{-1}{t} \cdot \left(y - x\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 1e+176)
   (fma (/ z t) (- y x) x)
   (fma (- z) (* (/ -1.0 t) (- y x)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 1e+176) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = fma(-z, ((-1.0 / t) * (y - x)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 1e+176)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = fma(Float64(-z), Float64(Float64(-1.0 / t) * Float64(y - x)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 1e+176], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[((-z) * N[(N[(-1.0 / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < 1e176

   1. Initial program 99.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 99.0

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

   4. Applied rewrites 99.0%

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

   if 1e176 < (/.f64 z t)

   1. Initial program 76.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. frac-2neg N/A

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

      7. div-inv N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. neg-mul-1 N/A

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

      13. associate-/r* N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, \frac{-1}{t} \cdot \left(y - x\right), x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(x - y\right) \cdot z, \frac{-1}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) 1e+176)
   (fma (/ z t) (- y x) x)
   (fma (* (- x y) z) (/ -1.0 t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= 1e+176) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = fma(((x - y) * z), (-1.0 / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= 1e+176)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = fma(Float64(Float64(x - y) * z), Float64(-1.0 / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], 1e+176], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] * z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < 1e176

   1. Initial program 99.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 99.0

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

   4. Applied rewrites 99.0%

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

   if 1e176 < (/.f64 z t)

   1. Initial program 76.9%

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

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

      5. associate-*r/ N/A

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

      6. frac-2neg N/A

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

      7. div-inv N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. associate-/r* N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(x - y\right) \cdot z, \frac{-1}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= y -4.8e+146) t_1 (if (<= y 8.5e+85) (- x (* (/ x t) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -4.8e+146) {
		tmp = t_1;
	} else if (y <= 8.5e+85) {
		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 * (z / t)
    if (y <= (-4.8d+146)) then
        tmp = t_1
    else if (y <= 8.5d+85) 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 * (z / t);
	double tmp;
	if (y <= -4.8e+146) {
		tmp = t_1;
	} else if (y <= 8.5e+85) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if y <= -4.8e+146:
		tmp = t_1
	elif y <= 8.5e+85:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (y <= -4.8e+146)
		tmp = t_1;
	elseif (y <= 8.5e+85)
		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 * (z / t);
	tmp = 0.0;
	if (y <= -4.8e+146)
		tmp = t_1;
	elseif (y <= 8.5e+85)
		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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+146], t$95$1, If[LessEqual[y, 8.5e+85], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000004e146 or 8.4999999999999994e85 < y

   1. Initial program 98.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 61.6

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

   5. Applied rewrites 61.6%

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

   7. Applied rewrites 66.8%

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

   if -4.8000000000000004e146 < y < 8.4999999999999994e85

   1. Initial program 94.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 75.1

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

   5. Applied rewrites 75.1%

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

Alternative 8: 47.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+57}:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= y -1.6e-20) t_1 (if (<= y 1.25e+57) (/ (* (- x) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -1.6e-20) {
		tmp = t_1;
	} else if (y <= 1.25e+57) {
		tmp = (-x * z) / 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 (y <= (-1.6d-20)) then
        tmp = t_1
    else if (y <= 1.25d+57) then
        tmp = (-x * z) / 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 (y <= -1.6e-20) {
		tmp = t_1;
	} else if (y <= 1.25e+57) {
		tmp = (-x * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if y <= -1.6e-20:
		tmp = t_1
	elif y <= 1.25e+57:
		tmp = (-x * z) / 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 (y <= -1.6e-20)
		tmp = t_1;
	elseif (y <= 1.25e+57)
		tmp = Float64(Float64(Float64(-x) * z) / 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 (y <= -1.6e-20)
		tmp = t_1;
	elseif (y <= 1.25e+57)
		tmp = (-x * z) / 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[y, -1.6e-20], t$95$1, If[LessEqual[y, 1.25e+57], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999985e-20 or 1.24999999999999993e57 < y

   1. Initial program 99.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 53.4

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

   5. Applied rewrites 53.4%

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

   7. Applied rewrites 57.7%

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

   if -1.59999999999999985e-20 < y < 1.24999999999999993e57

   1. Initial program 93.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 40.4%

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

Alternative 9: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{t} \cdot x\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z) t) x)))
   (if (<= x -2.3e+94) t_1 (if (<= x 3.8e+28) (* y (/ z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-z / t) * x;
	double tmp;
	if (x <= -2.3e+94) {
		tmp = t_1;
	} else if (x <= 3.8e+28) {
		tmp = y * (z / 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 = (-z / t) * x
    if (x <= (-2.3d+94)) then
        tmp = t_1
    else if (x <= 3.8d+28) then
        tmp = y * (z / 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 = (-z / t) * x;
	double tmp;
	if (x <= -2.3e+94) {
		tmp = t_1;
	} else if (x <= 3.8e+28) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-z / t) * x
	tmp = 0
	if x <= -2.3e+94:
		tmp = t_1
	elif x <= 3.8e+28:
		tmp = y * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-z) / t) * x)
	tmp = 0.0
	if (x <= -2.3e+94)
		tmp = t_1;
	elseif (x <= 3.8e+28)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-z / t) * x;
	tmp = 0.0;
	if (x <= -2.3e+94)
		tmp = t_1;
	elseif (x <= 3.8e+28)
		tmp = y * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-z) / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.3e+94], t$95$1, If[LessEqual[x, 3.8e+28], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e94 or 3.7999999999999999e28 < x

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 45.3

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

   5. Applied rewrites 45.3%

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

   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 36.2%

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

   10. Applied rewrites 41.7%

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

   if -2.3e94 < x < 3.7999999999999999e28

   1. Initial program 93.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 51.4

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

   5. Applied rewrites 51.4%

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

   7. Applied rewrites 54.6%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]
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 34.5

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

5. Applied rewrites 34.5%

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

7. Applied rewrites 37.7%

   \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]
8. 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 2024268 
(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))))