Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.7% → 97.7%

Time: 9.2s

Alternatives: 15

Speedup: 0.3×

• 24.9% 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: 92.7% 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: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- y x) (/ t z)))
     (if (<= t_1 5e+298) t_1 (* (- y x) (/ z t))))))

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)) {
		tmp = x + ((y - x) / (t / z));
	} else if (t_1 <= 5e+298) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / t);
	}
	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) {
		tmp = x + ((y - x) / (t / z));
	} else if (t_1 <= 5e+298) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y - x) / (t / z))
	elif t_1 <= 5e+298:
		tmp = t_1
	else:
		tmp = (y - x) * (z / t)
	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))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	elseif (t_1 <= 5e+298)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	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)
		tmp = x + ((y - x) / (t / z));
	elseif (t_1 <= 5e+298)
		tmp = t_1;
	else
		tmp = (y - x) * (z / t);
	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[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], t$95$1, N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 75.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 5.0000000000000003e298

   1. Initial program 99.3%

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

   if 5.0000000000000003e298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 82.6%

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

   2. Taylor expanded in t around 0 82.6%

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

      1. associate-/l* 100.0%

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

      2. clear-num 99.9%

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

      3. associate-/r/ 100.0%

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

      4. clear-num 100.0%

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

   4. Applied egg-rr 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 2: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+298}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+298)))
     (* (- y x) (/ z t))
     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 <= 5e+298)) {
		tmp = (y - x) * (z / t);
	} 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 <= 5e+298)) {
		tmp = (y - x) * (z / t);
	} 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 <= 5e+298):
		tmp = (y - x) * (z / t)
	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 <= 5e+298))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	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 <= 5e+298)))
		tmp = (y - x) * (z / t);
	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, 5e+298]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $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 5.0000000000000003e298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 78.8%

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

   2. Taylor expanded in t around 0 78.8%

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

      1. associate-/l* 95.8%

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

      2. clear-num 95.8%

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

      3. associate-/r/ 95.8%

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

      4. clear-num 95.8%

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

   4. Applied egg-rr 95.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 5.0000000000000003e298

   1. Initial program 99.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 5 \cdot 10^{+298}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-115} \lor \neg \left(z \leq 2.5 \cdot 10^{-79} \lor \neg \left(z \leq 1.4 \cdot 10^{-56}\right) \land z \leq 0.32\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-115)
         (not (or (<= z 2.5e-79) (and (not (<= z 1.4e-56)) (<= z 0.32)))))
   (* (- y x) (/ z t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-115) || !((z <= 2.5e-79) || (!(z <= 1.4e-56) && (z <= 0.32)))) {
		tmp = (y - x) * (z / 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 <= (-1.45d-115)) .or. (.not. (z <= 2.5d-79) .or. (.not. (z <= 1.4d-56)) .and. (z <= 0.32d0))) then
        tmp = (y - x) * (z / 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 <= -1.45e-115) || !((z <= 2.5e-79) || (!(z <= 1.4e-56) && (z <= 0.32)))) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-115) or not ((z <= 2.5e-79) or (not (z <= 1.4e-56) and (z <= 0.32))):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-115) || !((z <= 2.5e-79) || (!(z <= 1.4e-56) && (z <= 0.32))))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.45e-115) || ~(((z <= 2.5e-79) || (~((z <= 1.4e-56)) && (z <= 0.32)))))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-115], N[Not[Or[LessEqual[z, 2.5e-79], And[N[Not[LessEqual[z, 1.4e-56]], $MachinePrecision], LessEqual[z, 0.32]]]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e-115 or 2.5e-79 < z < 1.39999999999999997e-56 or 0.320000000000000007 < z

   1. Initial program 90.0%

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

   2. Taylor expanded in t around 0 76.7%

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

      1. associate-/l* 79.9%

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

      2. clear-num 79.8%

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

      3. associate-/r/ 79.8%

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

      4. clear-num 79.8%

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

   4. Applied egg-rr 79.8%

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

   if -1.4499999999999999e-115 < z < 2.5e-79 or 1.39999999999999997e-56 < z < 0.320000000000000007

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 73.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-115} \lor \neg \left(z \leq 2.5 \cdot 10^{-79} \lor \neg \left(z \leq 1.4 \cdot 10^{-56}\right) \land z \leq 0.32\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 55.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.35:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+236}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+277}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e-105)
   (/ y (/ t z))
   (if (<= z 0.35)
     x
     (if (<= z 3.7e+236)
       (* z (/ y t))
       (if (<= z 1.1e+277) (* z (- (/ x t))) (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e-105) {
		tmp = y / (t / z);
	} else if (z <= 0.35) {
		tmp = x;
	} else if (z <= 3.7e+236) {
		tmp = z * (y / t);
	} else if (z <= 1.1e+277) {
		tmp = z * -(x / t);
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.6d-105)) then
        tmp = y / (t / z)
    else if (z <= 0.35d0) then
        tmp = x
    else if (z <= 3.7d+236) then
        tmp = z * (y / t)
    else if (z <= 1.1d+277) then
        tmp = z * -(x / t)
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e-105) {
		tmp = y / (t / z);
	} else if (z <= 0.35) {
		tmp = x;
	} else if (z <= 3.7e+236) {
		tmp = z * (y / t);
	} else if (z <= 1.1e+277) {
		tmp = z * -(x / t);
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e-105:
		tmp = y / (t / z)
	elif z <= 0.35:
		tmp = x
	elif z <= 3.7e+236:
		tmp = z * (y / t)
	elif z <= 1.1e+277:
		tmp = z * -(x / t)
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e-105)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 0.35)
		tmp = x;
	elseif (z <= 3.7e+236)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.1e+277)
		tmp = Float64(z * Float64(-Float64(x / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.6e-105)
		tmp = y / (t / z);
	elseif (z <= 0.35)
		tmp = x;
	elseif (z <= 3.7e+236)
		tmp = z * (y / t);
	elseif (z <= 1.1e+277)
		tmp = z * -(x / t);
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e-105], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.35], x, If[LessEqual[z, 3.7e+236], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+277], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.6000000000000002e-105

   1. Initial program 88.5%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in y around inf 49.8%

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

      1. associate-/l* 55.1%

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

   5. Simplified 55.1%

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

   if -4.6000000000000002e-105 < z < 0.34999999999999998

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.0%

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

   if 0.34999999999999998 < z < 3.70000000000000014e236

   1. Initial program 86.8%

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

   2. Taylor expanded in t around 0 75.3%

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

   3. Taylor expanded in y around inf 49.6%

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

      1. associate-*l/ 56.5%

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

      2. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if 3.70000000000000014e236 < z < 1.09999999999999998e277

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. distribute-lft-in 74.2%

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

      3. *-rgt-identity 74.2%

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

      4. mul-1-neg 74.2%

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

      5. distribute-rgt-neg-in 74.2%

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

      6. unsub-neg 74.2%

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

   4. Simplified 74.2%

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

      1. associate-*r/ 82.5%

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

      2. add-cube-cbrt 82.0%

         \[\leadsto x - \frac{x \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} \]

      3. times-frac 82.1%

         \[\leadsto x - \color{blue}{\frac{x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}} \]

      4. add-sqr-sqrt 63.4%

         \[\leadsto x - \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      5. sqrt-unprod 63.7%

         \[\leadsto x - \frac{\color{blue}{\sqrt{x \cdot x}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      6. sqr-neg 63.7%

         \[\leadsto x - \frac{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      7. sqrt-unprod 0.5%

         \[\leadsto x - \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      8. add-sqr-sqrt 0.7%

         \[\leadsto x - \frac{\color{blue}{-x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      9. times-frac 0.7%

         \[\leadsto x - \color{blue}{\frac{\left(-x\right) \cdot z}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} \]

      10. *-commutative 0.7%

          \[\leadsto x - \frac{\color{blue}{z \cdot \left(-x\right)}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} \]

      11. add-cube-cbrt 0.7%

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

      12. associate-/l* 0.5%

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

      13. add-sqr-sqrt 0.3%

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

      14. sqrt-unprod 63.8%

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

      15. sqr-neg 63.8%

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

      16. sqrt-unprod 63.1%

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

      17. add-sqr-sqrt 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in z around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. associate-*r/ 82.3%

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

      3. distribute-rgt-neg-out 82.3%

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

      4. distribute-neg-frac 82.3%

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

   9. Simplified 82.3%

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

   if 1.09999999999999998e277 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   3. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

   5. Simplified 60.5%

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

      1. associate-/l* 41.4%

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

      2. associate-/r/ 60.5%

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

   7. Applied egg-rr 60.5%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.35:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+236}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+277}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-106}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+237}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+277}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e-106)
   (/ y (/ t z))
   (if (<= z 0.58)
     x
     (if (<= z 6.5e+237)
       (* z (/ y t))
       (if (<= z 1.15e+277) (/ (- z) (/ t x)) (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-106) {
		tmp = y / (t / z);
	} else if (z <= 0.58) {
		tmp = x;
	} else if (z <= 6.5e+237) {
		tmp = z * (y / t);
	} else if (z <= 1.15e+277) {
		tmp = -z / (t / x);
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.7d-106)) then
        tmp = y / (t / z)
    else if (z <= 0.58d0) then
        tmp = x
    else if (z <= 6.5d+237) then
        tmp = z * (y / t)
    else if (z <= 1.15d+277) then
        tmp = -z / (t / x)
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-106) {
		tmp = y / (t / z);
	} else if (z <= 0.58) {
		tmp = x;
	} else if (z <= 6.5e+237) {
		tmp = z * (y / t);
	} else if (z <= 1.15e+277) {
		tmp = -z / (t / x);
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e-106:
		tmp = y / (t / z)
	elif z <= 0.58:
		tmp = x
	elif z <= 6.5e+237:
		tmp = z * (y / t)
	elif z <= 1.15e+277:
		tmp = -z / (t / x)
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e-106)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 0.58)
		tmp = x;
	elseif (z <= 6.5e+237)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.15e+277)
		tmp = Float64(Float64(-z) / Float64(t / x));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e-106)
		tmp = y / (t / z);
	elseif (z <= 0.58)
		tmp = x;
	elseif (z <= 6.5e+237)
		tmp = z * (y / t);
	elseif (z <= 1.15e+277)
		tmp = -z / (t / x);
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e-106], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.58], x, If[LessEqual[z, 6.5e+237], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+277], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.70000000000000022e-106

   1. Initial program 88.5%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in y around inf 49.8%

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

      1. associate-/l* 55.1%

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

   5. Simplified 55.1%

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

   if -2.70000000000000022e-106 < z < 0.57999999999999996

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.0%

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

   if 0.57999999999999996 < z < 6.4999999999999999e237

   1. Initial program 86.8%

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

   2. Taylor expanded in t around 0 75.3%

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

   3. Taylor expanded in y around inf 49.6%

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

      1. associate-*l/ 56.5%

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

      2. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if 6.4999999999999999e237 < z < 1.14999999999999997e277

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate-/l* 91.7%

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

      2. clear-num 91.6%

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

      3. associate-/r/ 91.7%

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

      4. clear-num 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in y around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. associate-/l* 82.5%

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

      3. distribute-neg-frac 82.5%

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

   7. Simplified 82.5%

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

   if 1.14999999999999997e277 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   3. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

   5. Simplified 60.5%

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

      1. associate-/l* 41.4%

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

      2. associate-/r/ 60.5%

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

   7. Applied egg-rr 60.5%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-106}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+237}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+277}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 54.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.48:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+238}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-112)
   (/ y (/ t z))
   (if (<= z 0.48) x (if (<= z 3.1e+238) (* z (/ y t)) (- (/ (* x z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-112) {
		tmp = y / (t / z);
	} else if (z <= 0.48) {
		tmp = x;
	} else if (z <= 3.1e+238) {
		tmp = z * (y / t);
	} else {
		tmp = -((x * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.8d-112)) then
        tmp = y / (t / z)
    else if (z <= 0.48d0) then
        tmp = x
    else if (z <= 3.1d+238) then
        tmp = z * (y / t)
    else
        tmp = -((x * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-112) {
		tmp = y / (t / z);
	} else if (z <= 0.48) {
		tmp = x;
	} else if (z <= 3.1e+238) {
		tmp = z * (y / t);
	} else {
		tmp = -((x * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-112:
		tmp = y / (t / z)
	elif z <= 0.48:
		tmp = x
	elif z <= 3.1e+238:
		tmp = z * (y / t)
	else:
		tmp = -((x * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-112)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 0.48)
		tmp = x;
	elseif (z <= 3.1e+238)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = Float64(-Float64(Float64(x * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-112)
		tmp = y / (t / z);
	elseif (z <= 0.48)
		tmp = x;
	elseif (z <= 3.1e+238)
		tmp = z * (y / t);
	else
		tmp = -((x * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-112], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.48], x, If[LessEqual[z, 3.1e+238], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], (-N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e-112

   1. Initial program 88.5%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in y around inf 49.8%

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

      1. associate-/l* 55.1%

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

   5. Simplified 55.1%

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

   if -1.8e-112 < z < 0.47999999999999998

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.0%

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

   if 0.47999999999999998 < z < 3.10000000000000012e238

   1. Initial program 86.8%

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

   2. Taylor expanded in t around 0 75.3%

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

   3. Taylor expanded in y around inf 49.6%

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

      1. associate-*l/ 56.5%

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

      2. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if 3.10000000000000012e238 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

   3. Taylor expanded in y around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-rgt-neg-out 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.48:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+238}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x \cdot z}{t}\\ \end{array} \]

Alternative 7: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-11} \lor \neg \left(z \leq 9.6 \cdot 10^{+30}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e-11) (not (<= z 9.6e+30)))
   (* (- y x) (/ z t))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-11) || !(z <= 9.6e+30)) {
		tmp = (y - x) * (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 ((z <= (-1.25d-11)) .or. (.not. (z <= 9.6d+30))) then
        tmp = (y - x) * (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 ((z <= -1.25e-11) || !(z <= 9.6e+30)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e-11) or not (z <= 9.6e+30):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e-11) || !(z <= 9.6e+30))
		tmp = Float64(Float64(y - x) * 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 ((z <= -1.25e-11) || ~((z <= 9.6e+30)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e-11], N[Not[LessEqual[z, 9.6e+30]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000005e-11 or 9.5999999999999997e30 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. associate-/l* 83.6%

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

      2. clear-num 83.5%

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

      3. associate-/r/ 83.4%

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

      4. clear-num 83.5%

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

   4. Applied egg-rr 83.5%

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

   if -1.25000000000000005e-11 < z < 9.5999999999999997e30

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 90.3%

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

      1. associate-*l/ 25.6%

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

      2. *-commutative 25.6%

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

   4. Simplified 85.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-11} \lor \neg \left(z \leq 9.6 \cdot 10^{+30}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-11} \lor \neg \left(z \leq 3.9 \cdot 10^{+31}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-11) (not (<= z 3.9e+31)))
   (* (- y x) (/ z t))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-11) || !(z <= 3.9e+31)) {
		tmp = (y - x) * (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 ((z <= (-9d-11)) .or. (.not. (z <= 3.9d+31))) then
        tmp = (y - x) * (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 ((z <= -9e-11) || !(z <= 3.9e+31)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-11) or not (z <= 3.9e+31):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-11) || !(z <= 3.9e+31))
		tmp = Float64(Float64(y - x) * 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 ((z <= -9e-11) || ~((z <= 3.9e+31)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-11], N[Not[LessEqual[z, 3.9e+31]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999999e-11 or 3.89999999999999999e31 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. associate-/l* 83.6%

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

      2. clear-num 83.5%

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

      3. associate-/r/ 83.4%

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

      4. clear-num 83.5%

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

   4. Applied egg-rr 83.5%

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

   if -8.9999999999999999e-11 < z < 3.89999999999999999e31

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 90.3%

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

      1. associate-/l* 30.6%

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

   4. Simplified 89.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-11} \lor \neg \left(z \leq 3.9 \cdot 10^{+31}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+36} \lor \neg \left(y \leq 7.5 \cdot 10^{-140}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.65e+36) (not (<= y 7.5e-140)))
   (+ x (/ y (/ t z)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.65e+36) || !(y <= 7.5e-140)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.65d+36)) .or. (.not. (y <= 7.5d-140))) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.65e+36) || !(y <= 7.5e-140)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.65e+36) or not (y <= 7.5e-140):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.65e+36) || !(y <= 7.5e-140))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.65e+36) || ~((y <= 7.5e-140)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.65e+36], N[Not[LessEqual[y, 7.5e-140]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e36 or 7.4999999999999998e-140 < y

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 83.8%

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

      1. associate-/l* 58.2%

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

   4. Simplified 89.6%

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

   if -2.65e36 < y < 7.4999999999999998e-140

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. distribute-lft-in 83.5%

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

      3. *-rgt-identity 83.5%

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

      4. mul-1-neg 83.5%

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

      5. distribute-rgt-neg-in 83.5%

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

      6. unsub-neg 83.5%

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

   4. Simplified 83.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+36} \lor \neg \left(y \leq 7.5 \cdot 10^{-140}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+37} \lor \neg \left(y \leq 6.4 \cdot 10^{-141}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+37) (not (<= y 6.4e-141)))
   (+ x (/ y (/ t z)))
   (- x (/ z (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+37) || !(y <= 6.4e-141)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z / (t / 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 ((y <= (-1.8d+37)) .or. (.not. (y <= 6.4d-141))) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+37) || !(y <= 6.4e-141)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+37) or not (y <= 6.4e-141):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (z / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+37) || !(y <= 6.4e-141))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.8e+37) || ~((y <= 6.4e-141)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+37], N[Not[LessEqual[y, 6.4e-141]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999999e37 or 6.4000000000000003e-141 < y

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 83.8%

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

      1. associate-/l* 58.2%

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

   4. Simplified 89.6%

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

   if -1.79999999999999999e37 < y < 6.4000000000000003e-141

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. distribute-lft-in 83.5%

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

      3. *-rgt-identity 83.5%

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

      4. mul-1-neg 83.5%

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

      5. distribute-rgt-neg-in 83.5%

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

      6. unsub-neg 83.5%

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

   4. Simplified 83.5%

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

      1. associate-*r/ 85.2%

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

      2. add-cube-cbrt 85.0%

         \[\leadsto x - \frac{x \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} \]

      3. times-frac 86.9%

         \[\leadsto x - \color{blue}{\frac{x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}} \]

      4. add-sqr-sqrt 42.6%

         \[\leadsto x - \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      5. sqrt-unprod 57.3%

         \[\leadsto x - \frac{\color{blue}{\sqrt{x \cdot x}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      6. sqr-neg 57.3%

         \[\leadsto x - \frac{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      7. sqrt-unprod 25.3%

         \[\leadsto x - \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      8. add-sqr-sqrt 47.4%

         \[\leadsto x - \frac{\color{blue}{-x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}} \]

      9. times-frac 46.4%

         \[\leadsto x - \color{blue}{\frac{\left(-x\right) \cdot z}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} \]

      10. *-commutative 46.4%

          \[\leadsto x - \frac{\color{blue}{z \cdot \left(-x\right)}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} \]

      11. add-cube-cbrt 46.4%

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

      12. associate-/l* 47.3%

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

      13. add-sqr-sqrt 25.3%

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

      14. sqrt-unprod 57.3%

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

      15. sqr-neg 57.3%

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

      16. sqrt-unprod 42.6%

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

      17. add-sqr-sqrt 86.2%

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

   6. Applied egg-rr 86.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+37} \lor \neg \left(y \leq 6.4 \cdot 10^{-141}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 11: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e-11)
   (* z (- (/ y t) (/ x t)))
   (if (<= z 4.2e+30) (+ x (/ y (/ t z))) (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-11) {
		tmp = z * ((y / t) - (x / t));
	} else if (z <= 4.2e+30) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.3d-11)) then
        tmp = z * ((y / t) - (x / t))
    else if (z <= 4.2d+30) then
        tmp = x + (y / (t / z))
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-11) {
		tmp = z * ((y / t) - (x / t));
	} else if (z <= 4.2e+30) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e-11:
		tmp = z * ((y / t) - (x / t))
	elif z <= 4.2e+30:
		tmp = x + (y / (t / z))
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e-11)
		tmp = Float64(z * Float64(Float64(y / t) - Float64(x / t)));
	elseif (z <= 4.2e+30)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e-11)
		tmp = z * ((y / t) - (x / t));
	elseif (z <= 4.2e+30)
		tmp = x + (y / (t / z));
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e-11], N[(z * N[(N[(y / t), $MachinePrecision] - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+30], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000014e-11

   1. Initial program 83.8%

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

   2. Taylor expanded in z around inf 86.0%

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

   if -2.30000000000000014e-11 < z < 4.2e30

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 90.3%

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

      1. associate-/l* 30.6%

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

   4. Simplified 89.9%

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

   if 4.2e30 < z

   1. Initial program 88.8%

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

   2. Taylor expanded in t around 0 84.0%

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

      1. associate-/l* 87.1%

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

      2. clear-num 86.9%

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

      3. associate-/r/ 87.0%

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

      4. clear-num 87.1%

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

   4. Applied egg-rr 87.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 12: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-114} \lor \neg \left(z \leq 0.42\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e-114) (not (<= z 0.42))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e-114) || !(z <= 0.42)) {
		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 <= (-1.9d-114)) .or. (.not. (z <= 0.42d0))) 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 <= -1.9e-114) || !(z <= 0.42)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e-114) or not (z <= 0.42):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e-114) || !(z <= 0.42))
		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 <= -1.9e-114) || ~((z <= 0.42)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e-114], N[Not[LessEqual[z, 0.42]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e-114 or 0.419999999999999984 < z

   1. Initial program 89.2%

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

   2. Taylor expanded in t around 0 77.4%

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

   3. Taylor expanded in y around inf 49.1%

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

      1. associate-*l/ 53.6%

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

      2. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   if -1.8999999999999999e-114 < z < 0.419999999999999984

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-114} \lor \neg \left(z \leq 0.42\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-105} \lor \neg \left(z \leq 0.34\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.6e-105) (not (<= z 0.34))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-105) || !(z <= 0.34)) {
		tmp = y * (z / 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 <= (-4.6d-105)) .or. (.not. (z <= 0.34d0))) then
        tmp = y * (z / 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 <= -4.6e-105) || !(z <= 0.34)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.6e-105) or not (z <= 0.34):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.6e-105) || !(z <= 0.34))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.6e-105) || ~((z <= 0.34)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.6e-105], N[Not[LessEqual[z, 0.34]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000002e-105 or 0.340000000000000024 < z

   1. Initial program 89.2%

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

   2. Taylor expanded in t around 0 77.4%

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

   3. Taylor expanded in y around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

      1. associate-/l* 53.1%

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

      2. associate-/r/ 53.8%

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

   7. Applied egg-rr 53.8%

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

   if -4.6000000000000002e-105 < z < 0.340000000000000024

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.0%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-105} \lor \neg \left(z \leq 0.34\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.34:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e-105) (/ y (/ t z)) (if (<= z 0.34) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e-105) {
		tmp = y / (t / z);
	} else if (z <= 0.34) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.4d-105)) then
        tmp = y / (t / z)
    else if (z <= 0.34d0) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e-105) {
		tmp = y / (t / z);
	} else if (z <= 0.34) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e-105:
		tmp = y / (t / z)
	elif z <= 0.34:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e-105)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 0.34)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e-105)
		tmp = y / (t / z);
	elseif (z <= 0.34)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e-105], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.34], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000008e-105

   1. Initial program 88.5%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in y around inf 49.8%

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

      1. associate-/l* 55.1%

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

   5. Simplified 55.1%

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

   if -4.40000000000000008e-105 < z < 0.340000000000000024

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.0%

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

   if 0.340000000000000024 < z

   1. Initial program 90.0%

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

   2. Taylor expanded in t around 0 81.2%

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

   3. Taylor expanded in y around inf 48.3%

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

      1. *-commutative 48.3%

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

   5. Simplified 48.3%

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

      1. associate-/l* 49.8%

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

      2. associate-/r/ 52.6%

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

   7. Applied egg-rr 52.6%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 0.34:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 15: 38.6% 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 93.6%

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

2. Taylor expanded in z around 0 39.6%

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

3. Final simplification 39.6%

   \[\leadsto x \]

Developer target: 97.6% 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 2023185 
(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)))