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

Average Error: 11.0 → 0.5

Time: 12.1s

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+218}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 -1e+306)
     (+ x (* t (/ (- y z) (- a z))))
     (if (<= t_1 2e+218) (+ t_1 x) (+ x (/ (- y z) (/ (- a z) t)))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (t_1 <= 2e+218) {
		tmp = t_1 + x;
	} 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) / (a - z))
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) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if (t_1 <= (-1d+306)) then
        tmp = x + (t * ((y - z) / (a - z)))
    else if (t_1 <= 2d+218) then
        tmp = t_1 + x
    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) / (a - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (t_1 <= 2e+218) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -1e+306:
		tmp = x + (t * ((y - z) / (a - z)))
	elif t_1 <= 2e+218:
		tmp = t_1 + x
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -1e+306)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	elseif (t_1 <= 2e+218)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -1e+306)
		tmp = x + (t * ((y - z) / (a - z)));
	elseif (t_1 <= 2e+218)
		tmp = t_1 + x;
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+306], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+218], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	11.0
Target	0.6
Herbie	0.5

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.00000000000000002e306

   1. Initial program 63.4

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

   2. Simplified 0.2

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

      [Start] 63.4	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 0.2	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -1.00000000000000002e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2.00000000000000017e218

   1. Initial program 0.2

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

   if 2.00000000000000017e218 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 50.4

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

   2. Simplified 2.6

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

      [Start] 50.4	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-/l* [=>] 2.6	\[ x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 2 \cdot 10^{+218}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	1993

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+306} \lor \neg \left(t_1 \leq 2 \cdot 10^{+291}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

Alternative 2
Error	12.8
Cost	1232

\[\begin{array}{l} t_1 := x + \left(\left(y - z\right) \cdot t\right) \cdot \frac{1}{a}\\ t_2 := x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	13.7
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -0.000235:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 4
Error	12.2
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ t_2 := x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	15.0
Cost	976

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-26}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 6
Error	15.0
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -3 \cdot 10^{-11}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 7
Error	21.8
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-218}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-274}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+155}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	1.5
Cost	704

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

Alternative 9
Error	20.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-192}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 10
Error	27.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Error	51.5
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023016 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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