Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Average Accuracy: 97.7% → 98.4%

Time: 8.6s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-49} \lor \neg \left(y \leq -1 \cdot 10^{-291}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1e-49) (not (<= y -1e-291)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ x (/ (* y (- z t)) (- a t)))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1e-49) || !(y <= -1e-291)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + ((y * (z - t)) / (a - t));
	}
	return tmp;
}

Fortran

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) / (a - t)))
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 <= (-1d-49)) .or. (.not. (y <= (-1d-291)))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = x + ((y * (z - t)) / (a - t))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1e-49) || !(y <= -1e-291)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + ((y * (z - t)) / (a - t));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1e-49) or not (y <= -1e-291):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = x + ((y * (z - t)) / (a - t))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1e-49) || !(y <= -1e-291))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1e-49) || ~((y <= -1e-291)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = x + ((y * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1e-49], N[Not[LessEqual[y, -1e-291]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	97.7%
Target	99.3%
Herbie	98.4%

\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999936e-50 or -9.99999999999999962e-292 < y

   1. Initial program 98.0%

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

   if -9.99999999999999936e-50 < y < -9.99999999999999962e-292

   1. Initial program 96.6%

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

   2. Simplified 99.6%

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

      [Start] 96.6	\[ x + y \cdot \frac{z - t}{a - t} \]
      associate-*r/ [=>] 99.6	\[ x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-49} \lor \neg \left(y \leq -1 \cdot 10^{-291}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	63.2%
Cost	1242

\[\begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-226} \lor \neg \left(x \leq -1.75 \cdot 10^{-286}\right) \land \left(x \leq -2.6 \cdot 10^{-307} \lor \neg \left(x \leq 2.1 \cdot 10^{-187}\right) \land x \leq 1.7 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Accuracy	79.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+26} \lor \neg \left(t \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 3
Accuracy	84.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-108} \lor \neg \left(t \leq 8.8 \cdot 10^{-166}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4
Accuracy	78.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+26} \lor \neg \left(t \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 5
Accuracy	97.7%
Cost	704

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

Alternative 6
Accuracy	68.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+163}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	55.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023140 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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