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

Average Error: 10.5 → 0.8

Time: 13.6s

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-150}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

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 (- INFINITY))
     (+ x (* (- y z) (/ t (- a z))))
     (if (<= t_1 -2e-150) (+ x t_1) (+ x (* t (/ (- y z) (- a z))))))))

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 <= -((double) INFINITY)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (t_1 <= -2e-150) {
		tmp = x + t_1;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (t_1 <= -2e-150) {
		tmp = x + t_1;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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 <= -math.inf:
		tmp = x + ((y - z) * (t / (a - z)))
	elif t_1 <= -2e-150:
		tmp = x + t_1
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	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 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (t_1 <= -2e-150)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	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 <= -Inf)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (t_1 <= -2e-150)
		tmp = x + t_1;
	else
		tmp = x + (t * ((y - z) / (a - z)));
	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, (-Infinity)], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-150], N[(x + t$95$1), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	10.5
Target	0.5
Herbie	0.8

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 0.2

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

      [Start] 64.0	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      rational.json-simplify-2 [=>] 64.0	\[ x + \frac{\color{blue}{t \cdot \left(y - z\right)}}{a - z} \]
      rational.json-simplify-49 [=>] 0.2	\[ x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -2.00000000000000001e-150

   1. Initial program 0.1

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

   if -2.00000000000000001e-150 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 8.2

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

   2. Simplified 1.1

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

      [Start] 8.2	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      rational.json-simplify-49 [=>] 1.1	\[ x + \color{blue}{t \cdot \frac{y - z}{a - z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2 \cdot 10^{-150}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	14.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+127}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right) + x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Error	11.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3
Error	10.9
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4
Error	7.9
Cost	840

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	8.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;\left(-t \cdot \frac{y - z}{z}\right) + x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 6
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{-53}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 7
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-53}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 8
Error	1.3
Cost	704

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

Alternative 9
Error	1.1
Cost	704

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

Alternative 10
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-115}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11
Error	26.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-147}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	51.3
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023074 
(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))))