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

Average Accuracy: 83.2% → 96.7%

Time: 15.3s

Precision: binary64

Cost: 836

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e-256)
   (+ x (/ (- z t) (/ (- z a) y)))
   (+ x (/ y (/ (- z a) (- z t))))))

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 (a <= -1.05e-256) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x + (y / ((z - a) / (z - 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)) / (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 (a <= (-1.05d-256)) then
        tmp = x + ((z - t) / ((z - a) / y))
    else
        tmp = x + (y / ((z - a) / (z - 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)) / (z - a));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e-256) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	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 a <= -1.05e-256:
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = x + (y / ((z - a) / (z - t)))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e-256)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	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 (a <= -1.05e-256)
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = x + (y / ((z - a) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e-256], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	83.2%
Target	98.0%
Herbie	96.7%

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

Derivation

1. Split input into 2 regimes

2. if a < -1.05000000000000001e-256

   1. Initial program 82.9%

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

   2. Simplified 95.1%

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

      [Start] 82.9	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-*l/ [<=] 95.1	\[ x + \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   3. Applied egg-rr 95.0%

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

      [Start] 95.1	\[ x + \frac{y}{z - a} \cdot \left(z - t\right) \]
      *-commutative [=>] 95.1	\[ x + \color{blue}{\left(z - t\right) \cdot \frac{y}{z - a}} \]
      clear-num [=>] 94.7	\[ x + \left(z - t\right) \cdot \color{blue}{\frac{1}{\frac{z - a}{y}}} \]
      un-div-inv [=>] 95.0	\[ x + \color{blue}{\frac{z - t}{\frac{z - a}{y}}} \]

   if -1.05000000000000001e-256 < a

   1. Initial program 83.6%

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

   2. Simplified 98.1%

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

      [Start] 83.6	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 98.1	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	62.0%
Cost	2032

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := \frac{z - t}{\frac{z}{y}}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-215}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-284}:\\ \;\;\;\;\frac{-t}{\frac{z - a}{y}}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-282}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{-y}{\frac{a}{z - t}}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	63.0%
Cost	1900

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := y - y \cdot \frac{t}{z}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-223}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-185}:\\ \;\;\;\;\frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq 7.9 \cdot 10^{-174}:\\ \;\;\;\;\frac{-y}{\frac{a}{z - t}}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	62.1%
Cost	1768

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-216}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-282}:\\ \;\;\;\;\frac{-t}{\frac{z - a}{y}}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-282}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-142}:\\ \;\;\;\;\frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-118}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	74.2%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-144}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+166}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	74.9%
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-138}:\\ \;\;\;\;y + \left(x - \frac{t}{\frac{z}{y}}\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Accuracy	80.5%
Cost	972

\[\begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -3.25 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-204}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 7
Accuracy	96.6%
Cost	836

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-291}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]

Alternative 8
Accuracy	77.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -650000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Accuracy	95.1%
Cost	704

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

Alternative 10
Accuracy	68.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -480000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	57.2%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	54.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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