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

Average Accuracy: 98.0% → 99.1%

Time: 13.7s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-162} \lor \neg \left(y \leq 3 \cdot 10^{-33}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \]

FPCore

(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-162) (not (<= y 3e-33)))
   (+ x (* y (/ (- z t) (- z a))))
   (- x (/ (* y (- t z)) (- z a)))))

C

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-162) || !(y <= 3e-33)) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else {
		tmp = x - ((y * (t - z)) / (z - a));
	}
	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) / (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-162)) .or. (.not. (y <= 3d-33))) then
        tmp = x + (y * ((z - t) / (z - a)))
    else
        tmp = x - ((y * (t - z)) / (z - a))
    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) / (z - a)));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-162) || !(y <= 3e-33)) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else {
		tmp = x - ((y * (t - z)) / (z - a));
	}
	return tmp;
}

Python

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-162) or not (y <= 3e-33):
		tmp = x + (y * ((z - t) / (z - a)))
	else:
		tmp = x - ((y * (t - z)) / (z - a))
	return tmp

Julia

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-162) || !(y <= 3e-33))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

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-162) || ~((y <= 3e-33)))
		tmp = x + (y * ((z - t) / (z - a)));
	else
		tmp = x - ((y * (t - z)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

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-162], N[Not[LessEqual[y, 3e-33]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	98.0%
Target	98.1%
Herbie	99.1%

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

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000014e-162 or 3.0000000000000002e-33 < y

   1. Initial program 98.8%

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

   if -5.00000000000000014e-162 < y < 3.0000000000000002e-33

   1. Initial program 96.5%

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

   2. Simplified 99.5%

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

      [Start] 96.5	\[ x + y \cdot \frac{z - t}{z - a} \]
      associate-*r/ [=>] 99.5	\[ x + \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-162} \lor \neg \left(y \leq 3 \cdot 10^{-33}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	82.6%
Cost	4060

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z}}\\ t_2 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;t_2 \leq 10^{+197}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+235}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 2
Accuracy	82.3%
Cost	4060

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z}}\\ t_2 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;t_2 \leq 10^{+197}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+235}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3
Accuracy	82.3%
Cost	3544

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \frac{y \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;t_1 \leq 10^{+197}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+235}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4
Accuracy	86.9%
Cost	2124

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+177}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 5
Accuracy	64.8%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.00024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	64.8%
Cost	980

\[\begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 0.00024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	77.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-94}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Accuracy	77.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-95}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Accuracy	98.0%
Cost	704

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

Alternative 10
Accuracy	68.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-138}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Accuracy	55.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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)))))