Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Accuracy: 61.7% → 88.3%

Time: 25.7s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_1 \leq 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ y (* (- z a) (/ (- x y) t)))
     (if (<= t_1 -1e-260)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_1 1e+291) t_1 (+ x (* (- t z) (/ (- x y) (- a t))))))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t_1 <= -1e-260) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_1 <= 1e+291) {
		tmp = t_1;
	} else {
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t_1 <= -1e-260) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_1 <= 1e+291) {
		tmp = t_1;
	} else {
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y + ((z - a) * ((x - y) / t))
	elif t_1 <= -1e-260:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + ((x * (z - a)) / t)
	elif t_1 <= 1e+291:
		tmp = t_1
	else:
		tmp = x + ((t - z) * ((x - y) / (a - t)))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	elseif (t_1 <= -1e-260)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_1 <= 1e+291)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - z) * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y + ((z - a) * ((x - y) / t));
	elseif (t_1 <= -1e-260)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + ((x * (z - a)) / t);
	elseif (t_1 <= 1e+291)
		tmp = t_1;
	else
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-260], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+291], t$95$1, N[(x + N[(N[(t - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	61.7%
Target	85.9%
Herbie	88.3%

\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 0.0%

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

   2. Simplified 73.7%

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

      [Start] 0.0	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 0.0	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 73.7	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 73.7	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 73.7	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 35.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]

   4. Simplified 67.1%

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

      [Start] 35.3	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 35.3	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 35.3	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 35.3	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 35.3	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 35.3	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 35.3	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 66.1	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]
      associate-/r/ [=>] 67.1	\[ y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999961e-261 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999996e290

   1. Initial program 96.7%

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

   if -9.99999999999999961e-261 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 10.7%

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

   2. Simplified 11.3%

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

      [Start] 10.7	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 11.3	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Taylor expanded in t around inf 93.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

   4. Simplified 93.6%

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

      [Start] 93.6	\[ \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      +-commutative [=>] 93.6	\[ \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right)} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      associate--l+ [=>] 93.6	\[ \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]
      *-commutative [=>] 93.6	\[ y + \left(-1 \cdot \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 93.6	\[ y + \left(\color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 93.6	\[ y + \left(\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]
      div-sub [<=] 93.6	\[ y + \color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]
      distribute-lft-out-- [=>] 93.6	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

   5. Taylor expanded in x around inf 93.7%

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

   if 9.9999999999999996e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 4.8%

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

   2. Simplified 71.5%

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

      [Start] 4.8	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-*l/ [<=] 71.5	\[ x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+291}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.7%
Cost	8905

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-260} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 2
Accuracy	88.8%
Cost	2633

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-260} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 3
Accuracy	85.5%
Cost	1360

\[\begin{array}{l} t_1 := x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+176}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-280}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 4
Accuracy	69.7%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t}{a - t} \cdot \left(x - y\right)\\ t_2 := y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	73.2%
Cost	1232

\[\begin{array}{l} t_1 := x - \left(y - x\right) \cdot \frac{t}{a - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.95 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	73.6%
Cost	1232

\[\begin{array}{l} t_1 := x - \left(y - x\right) \cdot \frac{t}{a - t}\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+79}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 7
Accuracy	50.2%
Cost	844

\[\begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 21000000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	64.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-15} \lor \neg \left(a \leq 1.1 \cdot 10^{+19}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9
Accuracy	69.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-14} \lor \neg \left(a \leq 1.25 \cdot 10^{+19}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 10
Accuracy	60.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+36} \lor \neg \left(a \leq 1.3 \cdot 10^{+19}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11
Accuracy	41.8%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 35000000000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	44.5%
Cost	580

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+18}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	44.5%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Accuracy	3.0%
Cost	64

\[0 \]

Alternative 15
Accuracy	28.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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