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

Average Accuracy: 62.6% → 86.8%

Time: 38.6s

Precision: binary64

Cost: 1360

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y - x}{\frac{a - t}{z - t}}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-238}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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) (/ (- a t) (- z t)))))
        (t_2 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -3.9e+161)
     t_2
     (if (<= t -5.6e-118)
       t_1
       (if (<= t 5.8e-238)
         (- x (/ (* (- y x) (- t z)) (- a t)))
         (if (<= t 1.95e+182) t_1 t_2))))))

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) / ((a - t) / (z - t)));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -3.9e+161) {
		tmp = t_2;
	} else if (t <= -5.6e-118) {
		tmp = t_1;
	} else if (t <= 5.8e-238) {
		tmp = x - (((y - x) * (t - z)) / (a - t));
	} else if (t <= 1.95e+182) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 - x) * (z - t)) / (a - t))
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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) / ((a - t) / (z - t)))
    t_2 = y + ((x - y) / (t / (z - a)))
    if (t <= (-3.9d+161)) then
        tmp = t_2
    else if (t <= (-5.6d-118)) then
        tmp = t_1
    else if (t <= 5.8d-238) then
        tmp = x - (((y - x) * (t - z)) / (a - t))
    else if (t <= 1.95d+182) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

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) / ((a - t) / (z - t)));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -3.9e+161) {
		tmp = t_2;
	} else if (t <= -5.6e-118) {
		tmp = t_1;
	} else if (t <= 5.8e-238) {
		tmp = x - (((y - x) * (t - z)) / (a - t));
	} else if (t <= 1.95e+182) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) / ((a - t) / (z - t)))
	t_2 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -3.9e+161:
		tmp = t_2
	elif t <= -5.6e-118:
		tmp = t_1
	elif t <= 5.8e-238:
		tmp = x - (((y - x) * (t - z)) / (a - t))
	elif t <= 1.95e+182:
		tmp = t_1
	else:
		tmp = t_2
	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(y - x) / Float64(Float64(a - t) / Float64(z - t))))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -3.9e+161)
		tmp = t_2;
	elseif (t <= -5.6e-118)
		tmp = t_1;
	elseif (t <= 5.8e-238)
		tmp = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)));
	elseif (t <= 1.95e+182)
		tmp = t_1;
	else
		tmp = t_2;
	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) / ((a - t) / (z - t)));
	t_2 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -3.9e+161)
		tmp = t_2;
	elseif (t <= -5.6e-118)
		tmp = t_1;
	elseif (t <= 5.8e-238)
		tmp = x - (((y - x) * (t - z)) / (a - t));
	elseif (t <= 1.95e+182)
		tmp = t_1;
	else
		tmp = t_2;
	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[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+161], t$95$2, If[LessEqual[t, -5.6e-118], t$95$1, If[LessEqual[t, 5.8e-238], N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+182], t$95$1, t$95$2]]]]]]

Target

Original	62.6%
Target	85.8%
Herbie	86.8%

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

Derivation

1. Split input into 3 regimes

2. if t < -3.9000000000000002e161 or 1.9499999999999999e182 < t

   1. Initial program 24.5%

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

   2. Simplified 65.0%

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

      [Start] 24.5	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 24.5	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 65.0	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 65.0	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 65.0	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 62.1%

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

   4. Simplified 87.5%

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

      [Start] 62.1	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 62.1	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 62.1	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 62.1	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 62.1	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 62.1	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 62.1	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 87.5	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   if -3.9000000000000002e161 < t < -5.6e-118 or 5.7999999999999997e-238 < t < 1.9499999999999999e182

   1. Initial program 70.2%

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

   2. Simplified 85.3%

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

      [Start] 70.2	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 85.3	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   if -5.6e-118 < t < 5.7999999999999997e-238

   1. Initial program 90.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+161}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-118}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-238}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+182}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	86.3%
Cost	7500

\[\begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	86.3%
Cost	7368

\[\begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-242}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+187}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	88.3%
Cost	4432

\[\begin{array}{l} t_1 := y - \left(a - z\right) \cdot \frac{x - y}{t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	38.7%
Cost	2360

\[\begin{array}{l} t_1 := \frac{z}{\frac{a - t}{-x}}\\ t_2 := \frac{t}{a - t} \cdot \left(-y\right)\\ t_3 := x + x \cdot \frac{t}{a}\\ t_4 := \frac{y}{\frac{t}{t - z}}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-243}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-290}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-81}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+50}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	68.9%
Cost	1892

\[\begin{array}{l} t_1 := x + \frac{t}{a - t} \cdot \left(x - y\right)\\ t_2 := y - \left(a - z\right) \cdot \frac{x - y}{t}\\ t_3 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	69.2%
Cost	1892

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := x + \frac{t}{a - t} \cdot \left(x - y\right)\\ t_3 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	34.3%
Cost	1768

\[\begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-197}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-233}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-78}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	45.9%
Cost	1632

\[\begin{array}{l} t_1 := \frac{t}{a - t} \cdot \left(-y\right)\\ t_2 := z \cdot \frac{y - x}{a - t}\\ t_3 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-232}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	49.1%
Cost	1632

\[\begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_3 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{\frac{t}{t - z}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Accuracy	68.1%
Cost	1364

\[\begin{array}{l} t_1 := \frac{a}{y - x}\\ t_2 := x + \frac{z}{t_1}\\ t_3 := y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;x - \frac{t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Accuracy	46.4%
Cost	1304

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{t - z}}\\ t_2 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2800:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{t}{a - t} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	43.2%
Cost	1240

\[\begin{array}{l} t_1 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-276}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 6.9 \cdot 10^{-43}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 210000:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	46.4%
Cost	1240

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{t - z}}\\ t_2 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -7 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 200000:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	46.4%
Cost	1240

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{t - z}}\\ t_2 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 200000:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	49.9%
Cost	1236

\[\begin{array}{l} t_1 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+141}:\\ \;\;\;\;\frac{z}{\frac{a - t}{-x}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	54.7%
Cost	1236

\[\begin{array}{l} t_1 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+140}:\\ \;\;\;\;\frac{z}{\frac{a - t}{-x}}\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+110}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	54.7%
Cost	1236

\[\begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+176}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{+141}:\\ \;\;\;\;\frac{z}{\frac{a - t}{-x}}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+118}:\\ \;\;\;\;x + t \cdot \frac{x}{a - t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	86.4%
Cost	1228

\[\begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-242}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+187}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Accuracy	43.2%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-276}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-41}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1500000:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Accuracy	61.3%
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-274}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Accuracy	43.7%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Accuracy	42.5%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-124}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Accuracy	44.8%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Accuracy	3.0%
Cost	64

\[0 \]

Alternative 25
Accuracy	28.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(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))))