?

Average Error: 2.08% → 1.44%
Time: 10.1s
Precision: binary64
Cost: 969

?

\[x + y \cdot \frac{z - t}{z - a} \]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-44} \lor \neg \left(y \leq 5.6 \cdot 10^{+84}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e-44) (not (<= y 5.6e+84)))
   (+ x (* y (/ (- z t) (- z a))))
   (+ x (/ (* y (- z t)) (- z a)))))
double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-44) || !(y <= 5.6e+84)) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (z - a)))
end function
↓
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5d-44)) .or. (.not. (y <= 5.6d+84))) then
        tmp = x + (y * ((z - t) / (z - a)))
    else
        tmp = x + ((y * (z - t)) / (z - a))
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}
↓
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-44) || !(y <= 5.6e+84)) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))
↓
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5e-44) or not (y <= 5.6e+84):
		tmp = x + (y * ((z - t) / (z - a)))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	return tmp

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))))
end
↓
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e-44) || !(y <= 5.6e+84))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	end
	return tmp
end

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (z - a)));
end
↓
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5e-44) || ~((y <= 5.6e+84)))
		tmp = x + (y * ((z - t) / (z - a)));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e-44], N[Not[LessEqual[y, 5.6e+84]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -5 \cdot 10^{-44} \lor \neg \left(y \leq 5.6 \cdot 10^{+84}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\


\end{array}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.08%
Target1.97%
Herbie1.44%
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation?

  1. Split input into 2 regimes

  2. if y < -5.00000000000000039e-44 or 5.59999999999999963e84 < y

    1. Initial program 0.91

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

    if -5.00000000000000039e-44 < y < 5.59999999999999963e84

    1. Initial program 2.98

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

    2. Simplified1.85

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

      [Start]2.98

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

      associate-*r/ [=>]1.85

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

  4. Final simplification1.44

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-44} \lor \neg \left(y \leq 5.6 \cdot 10^{+84}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error18.87%
Cost3608
\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := y \cdot t_1\\ t_3 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z - a}\\ \end{array} \]
Alternative 2
Error17.83%
Cost3152
\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;t_1 \leq 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
Alternative 3
Error1.46%
Cost1992
\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+305}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
Alternative 4
Error31.65%
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -54000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
Alternative 5
Error21.51%
Cost713
\[\begin{array}{l} \mathbf{if}\;z \leq -45000000 \lor \neg \left(z \leq 1.1 \cdot 10^{+29}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
Alternative 6
Error21.69%
Cost713
\[\begin{array}{l} \mathbf{if}\;z \leq -60000000 \lor \neg \left(z \leq 4 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
Alternative 7
Error42.41%
Cost592
\[\begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-146}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-167}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 8
Error30.16%
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -58000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
Alternative 9
Error44.96%
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023089 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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