Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.8% → 97.5%

Time: 8.1s

Alternatives: 8

Speedup: 1.0×

• 24.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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(Float64(y - x) * 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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.8% accurate, 1.0× speedup

Math

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

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(Float64(y - x) * 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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z}{t}}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z}{t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right)\right) \]

   5. --lowering--.f64 98.4%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

4. Applied egg-rr 98.4%

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

Alternative 2: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 + z \cdot \frac{-1}{t}\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ 1.0 (* z (/ -1.0 t))))))
   (if (<= x -4.3e+18) t_1 (if (<= x 3.65e+133) (+ x (/ y (/ t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 + (z * (-1.0 / t)));
	double tmp;
	if (x <= -4.3e+18) {
		tmp = t_1;
	} else if (x <= 3.65e+133) {
		tmp = x + (y / (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 = x * (1.0d0 + (z * ((-1.0d0) / t)))
    if (x <= (-4.3d+18)) then
        tmp = t_1
    else if (x <= 3.65d+133) then
        tmp = x + (y / (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 = x * (1.0 + (z * (-1.0 / t)));
	double tmp;
	if (x <= -4.3e+18) {
		tmp = t_1;
	} else if (x <= 3.65e+133) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 + (z * (-1.0 / t)))
	tmp = 0
	if x <= -4.3e+18:
		tmp = t_1
	elif x <= 3.65e+133:
		tmp = x + (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 / t))))
	tmp = 0.0
	if (x <= -4.3e+18)
		tmp = t_1;
	elseif (x <= 3.65e+133)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 + (z * (-1.0 / t)));
	tmp = 0.0;
	if (x <= -4.3e+18)
		tmp = t_1;
	elseif (x <= 3.65e+133)
		tmp = x + (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 + N[(z * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+18], t$95$1, If[LessEqual[x, 3.65e+133], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e18 or 3.65e133 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 96.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 96.5%

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

      1. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{t}{z}}}\right)\right)\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{1}{t} \cdot \color{blue}{z}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{1}{t}\right), \color{blue}{z}\right)\right)\right) \]

      4. /-lowering-/.f64 96.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, t\right), z\right)\right)\right) \]

   7. Applied egg-rr 96.5%

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

   if -4.3e18 < x < 3.65e133

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 84.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 84.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      7. /-lowering-/.f64 88.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 88.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \frac{-1}{t}\right)\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \frac{-1}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z t)))))
   (if (<= x -1.45e+18) t_1 (if (<= x 7e+133) (+ x (/ y (/ t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -1.45e+18) {
		tmp = t_1;
	} else if (x <= 7e+133) {
		tmp = x + (y / (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 = x * (1.0d0 - (z / t))
    if (x <= (-1.45d+18)) then
        tmp = t_1
    else if (x <= 7d+133) then
        tmp = x + (y / (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 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -1.45e+18) {
		tmp = t_1;
	} else if (x <= 7e+133) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (z / t))
	tmp = 0
	if x <= -1.45e+18:
		tmp = t_1
	elif x <= 7e+133:
		tmp = x + (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (x <= -1.45e+18)
		tmp = t_1;
	elseif (x <= 7e+133)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (x <= -1.45e+18)
		tmp = t_1;
	elseif (x <= 7e+133)
		tmp = x + (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+18], t$95$1, If[LessEqual[x, 7e+133], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e18 or 6.9999999999999997e133 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 96.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 96.5%

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

   if -1.45e18 < x < 6.9999999999999997e133

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 84.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 84.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      7. /-lowering-/.f64 88.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 88.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z t)))))
   (if (<= x -5.5e+17) t_1 (if (<= x 2.6e+29) (+ x (/ (* z y) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -5.5e+17) {
		tmp = t_1;
	} else if (x <= 2.6e+29) {
		tmp = x + ((z * y) / 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 = x * (1.0d0 - (z / t))
    if (x <= (-5.5d+17)) then
        tmp = t_1
    else if (x <= 2.6d+29) then
        tmp = x + ((z * y) / 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 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -5.5e+17) {
		tmp = t_1;
	} else if (x <= 2.6e+29) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (z / t))
	tmp = 0
	if x <= -5.5e+17:
		tmp = t_1
	elif x <= 2.6e+29:
		tmp = x + ((z * y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (x <= -5.5e+17)
		tmp = t_1;
	elseif (x <= 2.6e+29)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (x <= -5.5e+17)
		tmp = t_1;
	elseif (x <= 2.6e+29)
		tmp = x + ((z * y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+17], t$95$1, If[LessEqual[x, 2.6e+29], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e17 or 2.6e29 < x

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 92.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 92.2%

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

   if -5.5e17 < x < 2.6e29

   1. Initial program 96.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 87.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 87.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e+147)
   (* z (/ (- y x) t))
   (if (<= y 7.5e+74) (* x (- 1.0 (/ z t))) (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+147) {
		tmp = z * ((y - x) / t);
	} else if (y <= 7.5e+74) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d+147)) then
        tmp = z * ((y - x) / t)
    else if (y <= 7.5d+74) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = (z / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+147) {
		tmp = z * ((y - x) / t);
	} else if (y <= 7.5e+74) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e+147:
		tmp = z * ((y - x) / t)
	elif y <= 7.5e+74:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e+147)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (y <= 7.5e+74)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e+147)
		tmp = z * ((y - x) / t);
	elseif (y <= 7.5e+74)
		tmp = x * (1.0 - (z / t));
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e+147], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+74], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e147

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 72.7%

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

   if -1.4e147 < y < 7.5e74

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 81.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 81.2%

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

   if 7.5e74 < y

   1. Initial program 89.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z}{t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right)\right) \]

      5. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      3. /-lowering-/.f64 77.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   7. Simplified 77.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+183}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+183)
   (/ (* z y) t)
   (if (<= y 6.3e+74) (* x (- 1.0 (/ z t))) (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+183) {
		tmp = (z * y) / t;
	} else if (y <= 6.3e+74) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.1d+183)) then
        tmp = (z * y) / t
    else if (y <= 6.3d+74) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = (z / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+183) {
		tmp = (z * y) / t;
	} else if (y <= 6.3e+74) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+183:
		tmp = (z * y) / t
	elif y <= 6.3e+74:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+183)
		tmp = Float64(Float64(z * y) / t);
	elseif (y <= 6.3e+74)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e+183)
		tmp = (z * y) / t;
	elseif (y <= 6.3e+74)
		tmp = x * (1.0 - (z / t));
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+183], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 6.3e+74], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.09999999999999995e183

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 73.7%

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

   if -1.09999999999999995e183 < y < 6.30000000000000016e74

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 80.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 80.9%

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

   if 6.30000000000000016e74 < y

   1. Initial program 89.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z}{t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right)\right) \]

      5. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      3. /-lowering-/.f64 77.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   7. Simplified 77.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+183}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.28e-12) x (if (<= t 2.3e+91) (* (/ z t) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.28e-12) {
		tmp = x;
	} else if (t <= 2.3e+91) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.28d-12)) then
        tmp = x
    else if (t <= 2.3d+91) then
        tmp = (z / t) * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.28e-12) {
		tmp = x;
	} else if (t <= 2.3e+91) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.28e-12:
		tmp = x
	elif t <= 2.3e+91:
		tmp = (z / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.28e-12)
		tmp = x;
	elseif (t <= 2.3e+91)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.28e-12)
		tmp = x;
	elseif (t <= 2.3e+91)
		tmp = (z / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.28e-12], x, If[LessEqual[t, 2.3e+91], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.28e-12 or 2.29999999999999991e91 < t

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 71.9%

      \[\leadsto \color{blue}{x} \]

   if -1.28e-12 < t < 2.29999999999999991e91

   1. Initial program 98.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z}{t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right)\right) \]

      5. --lowering--.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      3. /-lowering-/.f64 55.2%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   7. Simplified 55.2%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 92.8%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 44.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

  (+ x (/ (* (- y x) z) t)))