Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.1% → 99.0%

Time: 7.8s

Alternatives: 12

Speedup: 1.0×

• 24.7% 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: 93.1% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 4 \cdot 10^{+303}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+303)))
     (+ x (/ z (/ t (- y x))))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+303)) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+303)) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+303):
		tmp = x + (z / (t / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * z) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+303))
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((y - x) * z) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+303)))
		tmp = x + (z / (t / (y - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+303]], $MachinePrecision]], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0 or 4e303 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 82.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 4e303

   1. Initial program 98.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 4 \cdot 10^{+303}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-44} \lor \neg \left(z \leq 7.5 \cdot 10^{+15}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= z -4.1e+201)
     t_1
     (if (<= z -3.55e+28)
       (* x (/ (- z) t))
       (if (or (<= z -6.2e-44) (not (<= z 7.5e+15))) t_1 x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -4.1e+201) {
		tmp = t_1;
	} else if (z <= -3.55e+28) {
		tmp = x * (-z / t);
	} else if ((z <= -6.2e-44) || !(z <= 7.5e+15)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * (y / t)
    if (z <= (-4.1d+201)) then
        tmp = t_1
    else if (z <= (-3.55d+28)) then
        tmp = x * (-z / t)
    else if ((z <= (-6.2d-44)) .or. (.not. (z <= 7.5d+15))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -4.1e+201) {
		tmp = t_1;
	} else if (z <= -3.55e+28) {
		tmp = x * (-z / t);
	} else if ((z <= -6.2e-44) || !(z <= 7.5e+15)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if z <= -4.1e+201:
		tmp = t_1
	elif z <= -3.55e+28:
		tmp = x * (-z / t)
	elif (z <= -6.2e-44) or not (z <= 7.5e+15):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (z <= -4.1e+201)
		tmp = t_1;
	elseif (z <= -3.55e+28)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif ((z <= -6.2e-44) || !(z <= 7.5e+15))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (z <= -4.1e+201)
		tmp = t_1;
	elseif (z <= -3.55e+28)
		tmp = x * (-z / t);
	elseif ((z <= -6.2e-44) || ~((z <= 7.5e+15)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+201], t$95$1, If[LessEqual[z, -3.55e+28], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.2e-44], N[Not[LessEqual[z, 7.5e+15]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000002e201 or -3.55e28 < z < -6.19999999999999968e-44 or 7.5e15 < z

   1. Initial program 87.6%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 77.7%

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

   5. Taylor expanded in y around inf 53.9%

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

   if -4.1000000000000002e201 < z < -3.55e28

   1. Initial program 93.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. unsub-neg 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in z around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-frac-neg 56.0%

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

   9. Simplified 56.0%

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

   if -6.19999999999999968e-44 < z < 7.5e15

   1. Initial program 98.6%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+201}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-44} \lor \neg \left(z \leq 7.5 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-208} \lor \neg \left(x \leq 5.8 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e-208) (not (<= x 5.8e-103)))
   (* x (- 1.0 (/ z t)))
   (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e-208) || !(x <= 5.8e-103)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = z * (y / 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 ((x <= (-2.6d-208)) .or. (.not. (x <= 5.8d-103))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e-208) || !(x <= 5.8e-103)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.6e-208) or not (x <= 5.8e-103):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.6e-208) || !(x <= 5.8e-103))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.6e-208) || ~((x <= 5.8e-103)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.6e-208], N[Not[LessEqual[x, 5.8e-103]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000017e-208 or 5.7999999999999997e-103 < x

   1. Initial program 93.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

   6. Simplified 80.7%

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

   if -2.60000000000000017e-208 < x < 5.7999999999999997e-103

   1. Initial program 94.6%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around inf 72.4%

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

   5. Taylor expanded in y around inf 68.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-208} \lor \neg \left(x \leq 5.8 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-40} \lor \neg \left(z \leq 2.45 \cdot 10^{-68}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e-40) (not (<= z 2.45e-68)))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-40) || !(z <= 2.45e-68)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d-40)) .or. (.not. (z <= 2.45d-68))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-40) || !(z <= 2.45e-68)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e-40) or not (z <= 2.45e-68):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e-40) || !(z <= 2.45e-68))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e-40) || ~((z <= 2.45e-68)))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e-40], N[Not[LessEqual[z, 2.45e-68]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000021e-40 or 2.44999999999999988e-68 < z

   1. Initial program 90.0%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 77.9%

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

   5. Taylor expanded in y around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. sub-neg 77.9%

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

      4. div-sub 80.0%

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

   7. Simplified 80.0%

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

   if -6.20000000000000021e-40 < z < 2.44999999999999988e-68

   1. Initial program 98.5%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   6. Simplified 78.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-40} \lor \neg \left(z \leq 2.45 \cdot 10^{-68}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 5: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -26500 \lor \neg \left(x \leq 1.12 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -26500.0) (not (<= x 1.12e+30)))
   (* x (- 1.0 (/ z t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -26500.0) || !(x <= 1.12e+30)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z * (y / 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 ((x <= (-26500.0d0)) .or. (.not. (x <= 1.12d+30))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -26500.0) || !(x <= 1.12e+30)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -26500.0) or not (x <= 1.12e+30):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -26500.0) || !(x <= 1.12e+30))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -26500.0) || ~((x <= 1.12e+30)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -26500.0], N[Not[LessEqual[x, 1.12e+30]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -26500 or 1.12e30 < x

   1. Initial program 92.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 88.7%

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

      1. mul-1-neg 88.7%

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

      2. unsub-neg 88.7%

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

   6. Simplified 88.7%

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

   if -26500 < x < 1.12e30

   1. Initial program 95.3%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 83.2%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -26500 \lor \neg \left(x \leq 1.12 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+23} \lor \neg \left(y \leq 1.5 \cdot 10^{-107}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e+23) (not (<= y 1.5e-107)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+23) || !(y <= 1.5e-107)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3d+23)) .or. (.not. (y <= 1.5d-107))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+23) || !(y <= 1.5e-107)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e+23) or not (y <= 1.5e-107):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e+23) || !(y <= 1.5e-107))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e+23) || ~((y <= 1.5e-107)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e+23], N[Not[LessEqual[y, 1.5e-107]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000001e23 or 1.4999999999999999e-107 < y

   1. Initial program 92.4%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around inf 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

      1. associate-/r/ 87.3%

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

   8. Applied egg-rr 87.3%

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

   if -3.0000000000000001e23 < y < 1.4999999999999999e-107

   1. Initial program 95.3%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. unsub-neg 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+23} \lor \neg \left(y \leq 1.5 \cdot 10^{-107}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 7: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+24)
   (+ x (* y (/ z t)))
   (if (<= y 4e-110) (* x (- 1.0 (/ z t))) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+24) {
		tmp = x + (y * (z / t));
	} else if (y <= 4e-110) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.2d+24)) then
        tmp = x + (y * (z / t))
    else if (y <= 4d-110) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+24) {
		tmp = x + (y * (z / t));
	} else if (y <= 4e-110) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+24:
		tmp = x + (y * (z / t))
	elif y <= 4e-110:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+24)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (y <= 4e-110)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e+24)
		tmp = x + (y * (z / t));
	elseif (y <= 4e-110)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+24], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-110], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1999999999999997e24

   1. Initial program 90.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 82.9%

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

   6. Simplified 82.9%

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

      1. associate-/r/ 88.5%

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

   8. Applied egg-rr 88.5%

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

   if -5.1999999999999997e24 < y < 4.0000000000000002e-110

   1. Initial program 95.3%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. unsub-neg 87.5%

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

   6. Simplified 87.5%

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

   if 4.0000000000000002e-110 < y

   1. Initial program 93.5%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/l* 82.1%

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

   6. Simplified 82.1%

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

      1. associate-/r/ 86.6%

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

   8. Applied egg-rr 86.6%

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

      1. *-commutative 86.6%

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

      2. clear-num 86.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{t}{z}}} \]

      3. un-div-inv 86.6%

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

   10. Applied egg-rr 86.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 8: 93.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e+114) (* x (- 1.0 (/ z t))) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e+114) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z * ((y - x) / 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 (x <= (-6d+114)) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (z * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e+114) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e+114:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e+114)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e+114)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e+114], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000001e114

   1. Initial program 90.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 97.6%

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

      1. mul-1-neg 97.6%

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

      2. unsub-neg 97.6%

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

   6. Simplified 97.6%

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

   if -6.0000000000000001e114 < x

   1. Initial program 94.3%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 9: 93.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.6e+162) (* x (- 1.0 (/ z t))) (+ x (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.6e+162) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z / (t / (y - 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 (x <= (-4.6d+162)) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.6e+162) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.6e+162:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.6e+162)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.6e+162)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.6e+162], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.59999999999999987e162

   1. Initial program 93.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

   6. Simplified 96.6%

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

   if -4.59999999999999987e162 < x

   1. Initial program 93.8%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

      1. *-commutative 93.1%

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

      2. clear-num 93.0%

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

      3. un-div-inv 93.9%

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

   5. Applied egg-rr 93.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 10: 56.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-46} \lor \neg \left(z \leq 5.7 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e-46) (not (<= z 5.7e+16))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e-46) || !(z <= 5.7e+16)) {
		tmp = z * (y / t);
	} 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 ((z <= (-7.6d-46)) .or. (.not. (z <= 5.7d+16))) then
        tmp = z * (y / t)
    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 ((z <= -7.6e-46) || !(z <= 5.7e+16)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.6e-46) or not (z <= 5.7e+16):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e-46) || !(z <= 5.7e+16))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.6e-46) || ~((z <= 5.7e+16)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e-46], N[Not[LessEqual[z, 5.7e+16]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999993e-46 or 5.7e16 < z

   1. Initial program 89.2%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around inf 79.0%

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

   5. Taylor expanded in y around inf 51.2%

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

   if -7.5999999999999993e-46 < z < 5.7e16

   1. Initial program 98.6%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-46} \lor \neg \left(z \leq 5.7 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{\frac{t}{z}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) / (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 = x + ((y - x) / (t / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 12: 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 93.7%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in t around inf 38.0%

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

5. Final simplification 38.0%

   \[\leadsto x \]

Developer target: 97.5% accurate, 0.7× 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 2023318 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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)))))

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