Average Error: 1.4 → 0.7
Time: 10.9s
Precision: binary64
Cost: 969
\[x + y \cdot \frac{z - t}{z - a} \]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+35} \lor \neg \left(y \leq 10^{-151}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
(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 -5.5e+35) (not (<= y 1e-151)))
   (+ 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 <= -5.5e+35) || !(y <= 1e-151)) {
		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 <= (-5.5d+35)) .or. (.not. (y <= 1d-151))) 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 <= -5.5e+35) || !(y <= 1e-151)) {
		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 <= -5.5e+35) or not (y <= 1e-151):
		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 <= -5.5e+35) || !(y <= 1e-151))
		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 <= -5.5e+35) || ~((y <= 1e-151)))
		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, -5.5e+35], N[Not[LessEqual[y, 1e-151]], $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 -5.5 \cdot 10^{+35} \lor \neg \left(y \leq 10^{-151}\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

Original1.4
Target1.3
Herbie0.7
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.50000000000000001e35 or 9.9999999999999994e-152 < y

    1. Initial program 0.9

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

    if -5.50000000000000001e35 < y < 9.9999999999999994e-152

    1. Initial program 2.0

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

    2. Simplified0.5

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

      [Start]2.0

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

      associate-*r/ [=>]0.5

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+35} \lor \neg \left(y \leq 10^{-151}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error12.9
Cost1996
\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -2000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-31}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \]
Alternative 2
Error12.4
Cost1608
\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+239}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \]
Alternative 3
Error12.4
Cost1608
\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+239}:\\ \;\;\;\;\frac{-1}{\frac{z - a}{y \cdot t}}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \]
Alternative 4
Error1.0
Cost1220
\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{-1}{\frac{z - a}{y \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t_1\\ \end{array} \]
Alternative 5
Error15.9
Cost976
\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-55}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-70}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
Alternative 6
Error20.9
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-195}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
Alternative 7
Error14.5
Cost713
\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-55} \lor \neg \left(z \leq 6.8 \cdot 10^{-21}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
Alternative 8
Error20.9
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-165}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
Alternative 9
Error15.1
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-56}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
Alternative 10
Error20.2
Cost457
\[\begin{array}{l} \mathbf{if}\;z \leq -1.88 \cdot 10^{-124} \lor \neg \left(z \leq 5.2 \cdot 10^{-85}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 11
Error27.2
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-225}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 12
Error28.9
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2023016 
(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)))))