Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.9% → 99.1%

Time: 8.4s

Alternatives: 13

Speedup: 0.8×

• 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: 92.9% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- y x)) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* z (/ (- y x) t)))
     (if (<= t_1 5e+284) t_1 (+ x (/ (- y x) (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (z * ((y - x) / t));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z * ((y - x) / t));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((z * (y - x)) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (z * ((y - x) / t))
	elif t_1 <= 5e+284:
		tmp = t_1
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(z * Float64(y - x)) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((z * (y - x)) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (z * ((y - x) / t));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+284], t$95$1, N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $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 73.6%

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

      1. associate-*l/ 100.0%

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

   3. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 4.9999999999999999e284

   1. Initial program 99.2%

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

   if 4.9999999999999999e284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 89.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{z \cdot \left(y - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;x + \frac{z \cdot \left(y - x\right)}{t} \leq 5 \cdot 10^{+284}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 2: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. +-commutative 93.6%

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

   2. *-commutative 93.6%

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

   3. associate-*l/ 96.5%

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

   4. fma-def 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 3: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+295}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- y x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+295)))
     (+ x (* z (/ (- y x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+295)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+295)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((z * (y - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+295):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(z * Float64(y - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+295))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((z * (y - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+295)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+295]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $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 9.9999999999999998e294 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 81.0%

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

      1. associate-*l/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 9.9999999999999998e294

   1. Initial program 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{z \cdot \left(y - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{z \cdot \left(y - x\right)}{t} \leq 10^{+295}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]

Alternative 4: 47.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -126000000000:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -126000000000.0)
   (/ (* z y) t)
   (if (<= y 1.8e-217)
     (* (/ x t) (- z))
     (if (<= y 2.16e-100)
       x
       (if (<= y 2.6e+95)
         (* z (/ y t))
         (if (<= y 1.26e+162) x (* (/ z t) y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -126000000000.0) {
		tmp = (z * y) / t;
	} else if (y <= 1.8e-217) {
		tmp = (x / t) * -z;
	} else if (y <= 2.16e-100) {
		tmp = x;
	} else if (y <= 2.6e+95) {
		tmp = z * (y / t);
	} else if (y <= 1.26e+162) {
		tmp = x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-126000000000.0d0)) then
        tmp = (z * y) / t
    else if (y <= 1.8d-217) then
        tmp = (x / t) * -z
    else if (y <= 2.16d-100) then
        tmp = x
    else if (y <= 2.6d+95) then
        tmp = z * (y / t)
    else if (y <= 1.26d+162) then
        tmp = x
    else
        tmp = (z / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -126000000000.0) {
		tmp = (z * y) / t;
	} else if (y <= 1.8e-217) {
		tmp = (x / t) * -z;
	} else if (y <= 2.16e-100) {
		tmp = x;
	} else if (y <= 2.6e+95) {
		tmp = z * (y / t);
	} else if (y <= 1.26e+162) {
		tmp = x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -126000000000.0:
		tmp = (z * y) / t
	elif y <= 1.8e-217:
		tmp = (x / t) * -z
	elif y <= 2.16e-100:
		tmp = x
	elif y <= 2.6e+95:
		tmp = z * (y / t)
	elif y <= 1.26e+162:
		tmp = x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -126000000000.0)
		tmp = Float64(Float64(z * y) / t);
	elseif (y <= 1.8e-217)
		tmp = Float64(Float64(x / t) * Float64(-z));
	elseif (y <= 2.16e-100)
		tmp = x;
	elseif (y <= 2.6e+95)
		tmp = Float64(z * Float64(y / t));
	elseif (y <= 1.26e+162)
		tmp = x;
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -126000000000.0)
		tmp = (z * y) / t;
	elseif (y <= 1.8e-217)
		tmp = (x / t) * -z;
	elseif (y <= 2.16e-100)
		tmp = x;
	elseif (y <= 2.6e+95)
		tmp = z * (y / t);
	elseif (y <= 1.26e+162)
		tmp = x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -126000000000.0], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.8e-217], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 2.16e-100], x, If[LessEqual[y, 2.6e+95], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+162], x, N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.26e11

   1. Initial program 93.1%

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

   2. Taylor expanded in t around 0 76.6%

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

   3. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if -1.26e11 < y < 1.79999999999999991e-217

   1. Initial program 91.9%

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

   2. Taylor expanded in t around 0 68.7%

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

   3. Taylor expanded in y around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. distribute-rgt-neg-out 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in z around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-*r/ 61.2%

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

      3. distribute-rgt-neg-in 61.2%

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

   8. Simplified 61.2%

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

   if 1.79999999999999991e-217 < y < 2.1600000000000001e-100 or 2.5999999999999999e95 < y < 1.26e162

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 62.6%

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

   if 2.1600000000000001e-100 < y < 2.5999999999999999e95

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 63.0%

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

   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/ 49.9%

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

      2. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   if 1.26e162 < y

   1. Initial program 86.9%

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

   2. Taylor expanded in t around 0 65.7%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. associate-*r/ 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -126000000000:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]

Alternative 5: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-79} \lor \neg \left(z \leq 2.2 \cdot 10^{-174}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.12e-79) (not (<= z 2.2e-174))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e-79) || !(z <= 2.2e-174)) {
		tmp = z * ((y - x) / 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 <= (-1.12d-79)) .or. (.not. (z <= 2.2d-174))) then
        tmp = z * ((y - x) / 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 <= -1.12e-79) || !(z <= 2.2e-174)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.12e-79) or not (z <= 2.2e-174):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.12e-79) || !(z <= 2.2e-174))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.12e-79) || ~((z <= 2.2e-174)))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.12e-79], N[Not[LessEqual[z, 2.2e-174]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.11999999999999996e-79 or 2.20000000000000022e-174 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in t around 0 78.1%

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

      1. associate-*l/ 95.8%

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

   4. Applied egg-rr 80.0%

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

   if -1.11999999999999996e-79 < z < 2.20000000000000022e-174

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 68.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-79} \lor \neg \left(z \leq 2.2 \cdot 10^{-174}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4100000000000 \lor \neg \left(z \leq 13\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4100000000000.0) (not (<= z 13.0)))
   (* z (/ (- y x) t))
   (+ x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4100000000000.0) || !(z <= 13.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + ((z / t) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4100000000000.0d0)) .or. (.not. (z <= 13.0d0))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + ((z / t) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4100000000000.0) || !(z <= 13.0)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4100000000000.0) or not (z <= 13.0):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4100000000000.0) || !(z <= 13.0))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(Float64(z / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4100000000000.0) || ~((z <= 13.0)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4100000000000.0], N[Not[LessEqual[z, 13.0]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e12 or 13 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in t around 0 80.7%

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

      1. associate-*l/ 98.4%

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

   4. Applied egg-rr 88.3%

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

   if -4.1e12 < z < 13

   1. Initial program 98.4%

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

   2. Taylor expanded in y around inf 84.2%

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

      1. associate-*r/ 34.0%

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

   4. Simplified 83.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4100000000000 \lor \neg \left(z \leq 13\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \]

Alternative 7: 93.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+189}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 2.2e+189) (+ x (* z (/ (- y x) t))) (- x (* (/ z t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2.2e+189) {
		tmp = x + (z * ((y - x) / t));
	} 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 (x <= 2.2d+189) then
        tmp = x + (z * ((y - x) / t))
    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 (x <= 2.2e+189) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x - ((z / t) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 2.2e+189:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x - ((z / t) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 2.2e+189)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x - Float64(Float64(z / t) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 2.2e+189)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x - ((z / t) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 2.2e+189], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z / t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.20000000000000005e189

   1. Initial program 93.2%

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

      1. associate-*l/ 92.9%

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

   3. Applied egg-rr 92.9%

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

   if 2.20000000000000005e189 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-lft-identity 99.9%

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

      4. mul-1-neg 99.9%

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

      5. cancel-sign-sub-inv 99.9%

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

      6. *-commutative 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+189}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t} \cdot x\\ \end{array} \]

Alternative 8: 53.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-78} \lor \neg \left(z \leq 3.6 \cdot 10^{-174}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.8e-78) (not (<= z 3.6e-174))) (* (/ z t) y) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e-78) || !(z <= 3.6e-174)) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.8d-78)) .or. (.not. (z <= 3.6d-174))) then
        tmp = (z / t) * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e-78) || !(z <= 3.6e-174)) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.8e-78) or not (z <= 3.6e-174):
		tmp = (z / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.8e-78) || !(z <= 3.6e-174))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.8e-78) || ~((z <= 3.6e-174)))
		tmp = (z / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.8e-78], N[Not[LessEqual[z, 3.6e-174]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000023e-78 or 3.59999999999999999e-174 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in t around 0 78.1%

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

   3. Taylor expanded in y around inf 47.8%

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

      1. associate-*r/ 49.0%

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

   5. Simplified 49.0%

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

   if -6.80000000000000023e-78 < z < 3.59999999999999999e-174

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 68.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-78} \lor \neg \left(z \leq 3.6 \cdot 10^{-174}\right):\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e-80) (* z (/ y t)) (if (<= z 5.2e-174) x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-80) {
		tmp = z * (y / t);
	} else if (z <= 5.2e-174) {
		tmp = x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.2d-80)) then
        tmp = z * (y / t)
    else if (z <= 5.2d-174) then
        tmp = x
    else
        tmp = (z / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-80) {
		tmp = z * (y / t);
	} else if (z <= 5.2e-174) {
		tmp = x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e-80:
		tmp = z * (y / t)
	elif z <= 5.2e-174:
		tmp = x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e-80)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 5.2e-174)
		tmp = x;
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e-80)
		tmp = z * (y / t);
	elseif (z <= 5.2e-174)
		tmp = x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e-80], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-174], x, N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000003e-80

   1. Initial program 92.4%

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

   2. Taylor expanded in t around 0 80.6%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. associate-*l/ 42.4%

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

      2. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   if -4.20000000000000003e-80 < z < 5.2000000000000004e-174

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 68.4%

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

   if 5.2000000000000004e-174 < z

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 76.1%

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

   3. Taylor expanded in y around inf 51.0%

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

      1. associate-*r/ 54.2%

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

   5. Simplified 54.2%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]

Alternative 10: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e-80) (* z (/ y t)) (if (<= z 3.6e-174) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-80) {
		tmp = z * (y / t);
	} else if (z <= 3.6e-174) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.3d-80)) then
        tmp = z * (y / t)
    else if (z <= 3.6d-174) then
        tmp = x
    else
        tmp = 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 <= -1.3e-80) {
		tmp = z * (y / t);
	} else if (z <= 3.6e-174) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e-80:
		tmp = z * (y / t)
	elif z <= 3.6e-174:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e-80)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 3.6e-174)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.3e-80)
		tmp = z * (y / t);
	elseif (z <= 3.6e-174)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e-80], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-174], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e-80

   1. Initial program 92.4%

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

   2. Taylor expanded in t around 0 80.6%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. associate-*l/ 42.4%

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

      2. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   if -1.3e-80 < z < 3.59999999999999999e-174

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 68.4%

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

   if 3.59999999999999999e-174 < z

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 76.1%

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

   3. Taylor expanded in y around inf 51.0%

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

      1. associate-*r/ 54.2%

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

   5. Simplified 54.2%

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

      1. clear-num 54.2%

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

      2. un-div-inv 54.3%

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

   7. Applied egg-rr 54.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 11: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.08e-82) (* z (/ y t)) (if (<= z 5.9e-174) x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e-82) {
		tmp = z * (y / t);
	} else if (z <= 5.9e-174) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.08d-82)) then
        tmp = z * (y / t)
    else if (z <= 5.9d-174) then
        tmp = x
    else
        tmp = z / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e-82) {
		tmp = z * (y / t);
	} else if (z <= 5.9e-174) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.08e-82:
		tmp = z * (y / t)
	elif z <= 5.9e-174:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.08e-82)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 5.9e-174)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.08e-82)
		tmp = z * (y / t);
	elseif (z <= 5.9e-174)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.08e-82], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e-174], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.07999999999999996e-82

   1. Initial program 92.4%

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

   2. Taylor expanded in t around 0 80.6%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. associate-*l/ 42.4%

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

      2. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   if -1.07999999999999996e-82 < z < 5.9000000000000003e-174

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 68.4%

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

   if 5.9000000000000003e-174 < z

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 76.1%

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

   3. Taylor expanded in y around inf 51.0%

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

      1. associate-*r/ 54.2%

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

   5. Simplified 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*l/ 51.0%

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

      3. associate-/l* 54.5%

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

   7. Applied egg-rr 54.5%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 12: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e-83) (/ (* z y) t) (if (<= z 5.9e-174) x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-83) {
		tmp = (z * y) / t;
	} else if (z <= 5.9e-174) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.8d-83)) then
        tmp = (z * y) / t
    else if (z <= 5.9d-174) then
        tmp = x
    else
        tmp = z / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-83) {
		tmp = (z * y) / t;
	} else if (z <= 5.9e-174) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e-83:
		tmp = (z * y) / t
	elif z <= 5.9e-174:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e-83)
		tmp = Float64(Float64(z * y) / t);
	elseif (z <= 5.9e-174)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e-83)
		tmp = (z * y) / t;
	elseif (z <= 5.9e-174)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e-83], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5.9e-174], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.79999999999999977e-83

   1. Initial program 92.4%

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

   2. Taylor expanded in t around 0 80.6%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   if -3.79999999999999977e-83 < z < 5.9000000000000003e-174

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 68.4%

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

   if 5.9000000000000003e-174 < z

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 76.1%

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

   3. Taylor expanded in y around inf 51.0%

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

      1. associate-*r/ 54.2%

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

   5. Simplified 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*l/ 51.0%

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

      3. associate-/l* 54.5%

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

   7. Applied egg-rr 54.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 13: 38.5% 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 33.4%

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

3. Final simplification 33.4%

   \[\leadsto x \]

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 2023224 
(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)))