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

Percentage Accurate: 97.9% → 98.6%

Time: 6.1s

Alternatives: 11

Speedup: 0.5×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y - x) * Float64(z / t))) <= Float64(-Inf))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	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 + ((y - x) * (z / t))) <= -Inf)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.6%

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

   2. Taylor expanded in y around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. mul-1-neg 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-/l* 75.6%

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

      5. *-commutative 75.6%

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

      6. associate-/l* 67.7%

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

      7. div-sub 86.3%

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

      8. associate-/r/ 100.0%

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

      9. *-commutative 100.0%

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

   4. Simplified 100.0%

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

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

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.3%

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

   3. Applied egg-rr 98.3%

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

4. Final simplification 98.6%

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

Alternative 2: 98.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (<= t_1 (- INFINITY)) (+ x (* z (/ (- y x) 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)) {
		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 + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z * ((y - x) / 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:
		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(y - x) * Float64(z / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		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 + ((y - x) * (z / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		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[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], 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 y x) (/.f64 z t))) < -inf.0

   1. Initial program 85.6%

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

   2. Taylor expanded in y around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. mul-1-neg 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-/l* 75.6%

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

      5. *-commutative 75.6%

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

      6. associate-/l* 67.7%

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

      7. div-sub 86.3%

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

      8. associate-/r/ 100.0%

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

      9. *-commutative 100.0%

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

   4. Simplified 100.0%

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

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

   1. Initial program 98.1%

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

4. Final simplification 98.4%

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

Alternative 3: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.05 \cdot 10^{-27}\right):\\ \;\;\;\;x + x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-116) (not (<= x 1.05e-27)))
   (+ x (* x (/ z (- t))))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.05e-27)) {
		tmp = x + (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 ((x <= (-7.6d-116)) .or. (.not. (x <= 1.05d-27))) then
        tmp = x + (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 ((x <= -7.6e-116) || !(x <= 1.05e-27)) {
		tmp = x + (x * (z / -t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-116) or not (x <= 1.05e-27):
		tmp = x + (x * (z / -t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-116) || !(x <= 1.05e-27))
		tmp = Float64(x + Float64(x * Float64(z / Float64(-t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-116) || ~((x <= 1.05e-27)))
		tmp = x + (x * (z / -t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-116], N[Not[LessEqual[x, 1.05e-27]], $MachinePrecision]], N[(x + N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000003e-116 or 1.05000000000000008e-27 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r/ 90.7%

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

      4. distribute-rgt-neg-in 90.7%

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

      5. distribute-frac-neg 90.7%

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

      6. neg-mul-1 90.7%

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

      7. *-commutative 90.7%

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

      8. associate-/l* 90.7%

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

      9. metadata-eval 90.7%

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

      10. associate-/l* 90.7%

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

      11. *-commutative 90.7%

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

      12. neg-mul-1 90.7%

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

      13. /-rgt-identity 90.7%

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

   4. Simplified 90.7%

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

   if -7.6000000000000003e-116 < x < 1.05000000000000008e-27

   1. Initial program 91.3%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.9%

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

   3. Applied egg-rr 91.9%

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

   4. Taylor expanded in y around inf 87.0%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.05 \cdot 10^{-27}\right):\\ \;\;\;\;x + x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.6 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{x}{\frac{t}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-116) (not (<= x 1.6e-27)))
   (+ x (/ x (/ t (- z))))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.6e-27)) {
		tmp = x + (x / (t / -z));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.6d-116)) .or. (.not. (x <= 1.6d-27))) then
        tmp = x + (x / (t / -z))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.6e-27)) {
		tmp = x + (x / (t / -z));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-116) or not (x <= 1.6e-27):
		tmp = x + (x / (t / -z))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-116) || !(x <= 1.6e-27))
		tmp = Float64(x + Float64(x / Float64(t / Float64(-z))));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-116) || ~((x <= 1.6e-27)))
		tmp = x + (x / (t / -z));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-116], N[Not[LessEqual[x, 1.6e-27]], $MachinePrecision]], N[(x + N[(x / N[(t / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000003e-116 or 1.59999999999999995e-27 < x

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. associate-/l* 90.9%

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

      2. div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in y around 0 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*r/ 84.9%

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

      3. neg-mul-1 84.9%

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

      4. distribute-rgt-neg-in 84.9%

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

      5. associate-/l* 90.7%

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

   8. Simplified 90.7%

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

   if -7.6000000000000003e-116 < x < 1.59999999999999995e-27

   1. Initial program 91.3%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.9%

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

   3. Applied egg-rr 91.9%

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

   4. Taylor expanded in y around inf 87.0%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.6 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{x}{\frac{t}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 3 \cdot 10^{-27}\right):\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-116) (not (<= x 3e-27)))
   (- x (/ z (/ t x)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 3e-27)) {
		tmp = x - (z / (t / x));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.6d-116)) .or. (.not. (x <= 3d-27))) then
        tmp = x - (z / (t / x))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 3e-27)) {
		tmp = x - (z / (t / x));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-116) or not (x <= 3e-27):
		tmp = x - (z / (t / x))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-116) || !(x <= 3e-27))
		tmp = Float64(x - Float64(z / Float64(t / x)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-116) || ~((x <= 3e-27)))
		tmp = x - (z / (t / x));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-116], N[Not[LessEqual[x, 3e-27]], $MachinePrecision]], N[(x - N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000003e-116 or 3.0000000000000001e-27 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 86.4%

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

   4. Simplified 86.4%

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

   if -7.6000000000000003e-116 < x < 3.0000000000000001e-27

   1. Initial program 91.3%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.9%

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

   3. Applied egg-rr 91.9%

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

   4. Taylor expanded in y around inf 87.0%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 3 \cdot 10^{-27}\right):\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-136}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-136) (+ x (* z (/ y t))) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-136) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (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 (y <= (-1.3d-136)) then
        tmp = x + (z * (y / t))
    else
        tmp = x + (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 (y <= -1.3e-136) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-136:
		tmp = x + (z * (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-136)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-136)
		tmp = x + (z * (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-136], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999998e-136

   1. Initial program 93.7%

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

      1. clear-num 93.6%

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

      2. un-div-inv 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 83.3%

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

      2. *-commutative 83.3%

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

   6. Simplified 83.3%

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

   if -1.29999999999999998e-136 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 67.0%

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

      1. associate-*r/ 71.0%

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

   4. Simplified 71.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-136}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-129}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e-129) (+ x (* z (/ y t))) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-129) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.6d-129)) then
        tmp = x + (z * (y / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-129) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e-129:
		tmp = x + (z * (y / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e-129)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e-129)
		tmp = x + (z * (y / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e-129], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999999e-129

   1. Initial program 93.6%

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

      1. clear-num 93.5%

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

      2. un-div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-*l/ 83.1%

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

      2. *-commutative 83.1%

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

   6. Simplified 83.1%

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

   if -4.5999999999999999e-129 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 71.1%

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

   4. Simplified 71.1%

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

      1. clear-num 71.1%

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

      2. div-inv 71.2%

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

   6. Applied egg-rr 71.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-129}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 8: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-129) (+ x (/ z (/ t y))) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-129) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d-129)) then
        tmp = x + (z / (t / y))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-129) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-129:
		tmp = x + (z / (t / y))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-129)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e-129)
		tmp = x + (z / (t / y));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-129], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000034e-129

   1. Initial program 93.6%

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

      1. clear-num 93.5%

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

      2. un-div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-*l/ 83.1%

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

      2. *-commutative 83.1%

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

   6. Simplified 83.1%

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

      1. clear-num 83.1%

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

      2. un-div-inv 83.2%

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

   8. Applied egg-rr 83.2%

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

   if -5.80000000000000034e-129 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 71.1%

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

   4. Simplified 71.1%

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

      1. clear-num 71.1%

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

      2. div-inv 71.2%

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

   6. Applied egg-rr 71.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

2. Taylor expanded in y around 0 89.7%

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

   1. +-commutative 89.7%

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

   2. mul-1-neg 89.7%

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

   3. unsub-neg 89.7%

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

   4. associate-/l* 88.7%

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

   5. *-commutative 88.7%

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

   6. associate-/l* 91.0%

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

   7. div-sub 96.5%

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

   8. associate-/r/ 95.6%

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

   9. *-commutative 95.6%

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

4. Simplified 95.6%

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

5. Final simplification 95.6%

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

Alternative 10: 77.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

2. Taylor expanded in y around inf 70.1%

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

   1. associate-*r/ 73.5%

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

4. Simplified 73.5%

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

5. Final simplification 73.5%

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

Alternative 11: 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 96.3%

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

2. Taylor expanded in y around inf 70.1%

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

   1. associate-*r/ 73.5%

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

4. Simplified 73.5%

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

5. Taylor expanded in x around inf 37.6%

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

6. Final simplification 37.6%

   \[\leadsto x \]

Developer target: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t_1 < -1013646692435.8867:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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