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

Percentage Accurate: 97.6% → 97.6%

Time: 7.4s

Alternatives: 11

Speedup: 1.1×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 98.6

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

4. Applied rewrites 98.6%

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

Alternative 2: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 0.0002:\\ \;\;\;\;y \cdot \frac{z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -10000.0)
     t_1
     (if (<= (/ z t) 0.0002) (+ (* 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) <= -10000.0) {
		tmp = t_1;
	} else if ((z / t) <= 0.0002) {
		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) <= (-10000.0d0)) then
        tmp = t_1
    else if ((z / t) <= 0.0002d0) 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) <= -10000.0) {
		tmp = t_1;
	} else if ((z / t) <= 0.0002) {
		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) <= -10000.0:
		tmp = t_1
	elif (z / t) <= 0.0002:
		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) <= -10000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 0.0002)
		tmp = Float64(Float64(y * Float64(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) <= -10000.0)
		tmp = t_1;
	elseif ((z / t) <= 0.0002)
		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], -10000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 0.0002], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e4 or 2.0000000000000001e-4 < (/.f64 z t)

   1. Initial program 98.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 91.4

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

   5. Applied rewrites 91.4%

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

   7. Applied rewrites 97.4%

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

   if -1e4 < (/.f64 z t) < 2.0000000000000001e-4

   1. Initial program 98.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 98.8

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 89.4

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

   4. Applied rewrites 89.4%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 97.5

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

   7. Applied rewrites 97.5%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.0002:\\ \;\;\;\;y \cdot \frac{z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -10000.0)
     t_1
     (if (<= (/ z t) 0.0002) (fma (/ 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) <= -10000.0) {
		tmp = t_1;
	} else if ((z / t) <= 0.0002) {
		tmp = fma((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) <= -10000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 0.0002)
		tmp = fma(Float64(y / t), z, x);
	else
		tmp = t_1;
	end
	return 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], -10000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 0.0002], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e4 or 2.0000000000000001e-4 < (/.f64 z t)

   1. Initial program 98.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 91.4

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

   5. Applied rewrites 91.4%

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

   7. Applied rewrites 97.4%

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

   if -1e4 < (/.f64 z t) < 2.0000000000000001e-4

   1. Initial program 98.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 98.8

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 89.4

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

   4. Applied rewrites 89.4%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 92.2

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

   7. Applied rewrites 92.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 92.2

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

   9. Applied rewrites 92.2%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+173)
   (* y (/ z t))
   (if (<= (/ z t) -10000.0) (* (- x) (/ z t)) (fma (/ y t) z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+173) {
		tmp = y * (z / t);
	} else if ((z / t) <= -10000.0) {
		tmp = -x * (z / t);
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+173)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= -10000.0)
		tmp = Float64(Float64(-x) * Float64(z / t));
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+173], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -10000.0], N[((-x) * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e173

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lower-+.f64 100.0

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   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 69.6

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

   7. Applied rewrites 69.6%

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

   if -2e173 < (/.f64 z t) < -1e4

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 88.9

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

   5. Applied rewrites 88.9%

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

   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 68.1%

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

   10. Applied rewrites 68.1%

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

   if -1e4 < (/.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. lower-+.f64 98.2

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 90.5

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 78.2

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

   7. Applied rewrites 78.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 78.2

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

   9. Applied rewrites 78.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+173)
   (* y (/ z t))
   (if (<= (/ z t) -10000.0) (/ (* (- x) z) t) (fma (/ y t) z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+173) {
		tmp = y * (z / t);
	} else if ((z / t) <= -10000.0) {
		tmp = (-x * z) / t;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+173)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= -10000.0)
		tmp = Float64(Float64(Float64(-x) * z) / t);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+173], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -10000.0], N[(N[((-x) * z), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e173

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lower-+.f64 100.0

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   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 69.6

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

   7. Applied rewrites 69.6%

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

   if -2e173 < (/.f64 z t) < -1e4

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 88.9

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

   5. Applied rewrites 88.9%

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

   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 68.1%

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

   if -1e4 < (/.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. lower-+.f64 98.2

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 90.5

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 78.2

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

   7. Applied rewrites 78.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 78.2

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

   9. Applied rewrites 78.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\frac{\left(-x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+173)
   (* y (/ z t))
   (if (<= (/ z t) -5e+26) (* (/ (- x) t) z) (fma (/ y t) z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+173) {
		tmp = y * (z / t);
	} else if ((z / t) <= -5e+26) {
		tmp = (-x / t) * z;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+173)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= -5e+26)
		tmp = Float64(Float64(Float64(-x) / t) * z);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+173], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+26], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e173

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. lower-+.f64 100.0

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   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 69.6

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

   7. Applied rewrites 69.6%

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

   if -2e173 < (/.f64 z t) < -5.0000000000000001e26

   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 90.5

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

   5. Applied rewrites 90.5%

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

   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 61.2%

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

   if -5.0000000000000001e26 < (/.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. lower-+.f64 98.2

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 89.7

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

   4. Applied rewrites 89.7%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 77.6

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

   7. Applied rewrites 77.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 77.6

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

   9. Applied rewrites 77.6%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -4e-20) t_1 (if (<= (/ z t) 5e-23) (/ (* 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) <= -4e-20) {
		tmp = t_1;
	} else if ((z / t) <= 5e-23) {
		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) <= (-4d-20)) then
        tmp = t_1
    else if ((z / t) <= 5d-23) 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) <= -4e-20) {
		tmp = t_1;
	} else if ((z / t) <= 5e-23) {
		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) <= -4e-20:
		tmp = t_1
	elif (z / t) <= 5e-23:
		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) <= -4e-20)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-23)
		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) <= -4e-20)
		tmp = t_1;
	elseif ((z / t) <= 5e-23)
		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], -4e-20], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-23], N[(N[(x * t), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -3.99999999999999978e-20 or 5.0000000000000002e-23 < (/.f64 z t)

   1. Initial program 98.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 98.5

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 89.6

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

   4. Applied rewrites 89.6%

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

   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 54.6

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

   7. Applied rewrites 54.6%

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

   if -3.99999999999999978e-20 < (/.f64 z t) < 5.0000000000000002e-23

   1. Initial program 98.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 98.7

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. associate-/r/ N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. lower-/.f64 91.0

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

   4. Applied rewrites 91.0%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 82.5

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 65.0%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-54}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.3e-54) (* (/ y t) z) (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.3e-54) {
		tmp = (y / t) * z;
	} 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 (t <= (-4.3d-54)) then
        tmp = (y / t) * z
    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 (t <= -4.3e-54) {
		tmp = (y / t) * z;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.3e-54:
		tmp = (y / t) * z
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.3e-54)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.3e-54)
		tmp = (y / t) * z;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.3e-54], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3e-54

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   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 27.3

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

   5. Applied rewrites 27.3%

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

   if -4.3e-54 < t

   1. Initial program 98.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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 38.1

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

   5. Applied rewrites 38.1%

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

   7. Applied rewrites 42.9%

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

Alternative 9: 73.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 98.6

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

   4. lift-*.f64 N/A

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

   5. lift-/.f64 N/A

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

   6. clear-num N/A

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

   7. associate-/r/ N/A

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

   8. associate-*r* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. associate-*l/ N/A

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

   12. *-lft-identity N/A

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

   13. lower-/.f64 90.2

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

4. Applied rewrites 90.2%

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

5. Taylor expanded in y around inf

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

   1. lower-/.f64 69.9

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

7. Applied rewrites 69.9%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lower-fma.f64 69.9

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

9. Applied rewrites 69.9%

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

Alternative 10: 41.2% 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 98.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 98.6

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

   4. lift-*.f64 N/A

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

   5. lift-/.f64 N/A

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

   6. clear-num N/A

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

   7. associate-/r/ N/A

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

   8. associate-*r* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. associate-*l/ N/A

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

   12. *-lft-identity N/A

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

   13. lower-/.f64 90.2

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

4. Applied rewrites 90.2%

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

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 39.8

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

7. Applied rewrites 39.8%

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

8. Final simplification 39.8%

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

Alternative 11: 38.4% 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 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 35.4

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

5. Applied rewrites 35.4%

   \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]
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 2024277 
(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))))