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

Average Error: 38.33% → 10.02%

Time: 24.4s

Precision: binary64

Cost: 2505

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+171} \lor \neg \left(t \leq 10^{+167}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{a}{\frac{t}{\frac{a}{t}}} + \left(\left(y + \frac{x - y}{\frac{t}{z - a}}\right) - \frac{a}{\frac{\frac{t}{\frac{z}{t}}}{y - x}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + \left(x + x \cdot \frac{t - z}{a - t}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+171) (not (<= t 1e+167)))
   (+
    (* (- y x) (/ a (/ t (/ a t))))
    (- (+ y (/ (- x y) (/ t (- z a)))) (/ a (/ (/ t (/ z t)) (- y x)))))
   (+ (* y (/ (- z t) (- a t))) (+ x (* x (/ (- t z) (- 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 tmp;
	if ((t <= -1.05e+171) || !(t <= 1e+167)) {
		tmp = ((y - x) * (a / (t / (a / t)))) + ((y + ((x - y) / (t / (z - a)))) - (a / ((t / (z / t)) / (y - x))));
	} else {
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - 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 - 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) :: tmp
    if ((t <= (-1.05d+171)) .or. (.not. (t <= 1d+167))) then
        tmp = ((y - x) * (a / (t / (a / t)))) + ((y + ((x - y) / (t / (z - a)))) - (a / ((t / (z / t)) / (y - x))))
    else
        tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - 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 - x) * (z - t)) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+171) || !(t <= 1e+167)) {
		tmp = ((y - x) * (a / (t / (a / t)))) + ((y + ((x - y) / (t / (z - a)))) - (a / ((t / (z / t)) / (y - x))));
	} else {
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (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):
	tmp = 0
	if (t <= -1.05e+171) or not (t <= 1e+167):
		tmp = ((y - x) * (a / (t / (a / t)))) + ((y + ((x - y) / (t / (z - a)))) - (a / ((t / (z / t)) / (y - x))))
	else:
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (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)
	tmp = 0.0
	if ((t <= -1.05e+171) || !(t <= 1e+167))
		tmp = Float64(Float64(Float64(y - x) * Float64(a / Float64(t / Float64(a / t)))) + Float64(Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a)))) - Float64(a / Float64(Float64(t / Float64(z / t)) / Float64(y - x)))));
	else
		tmp = Float64(Float64(y * Float64(Float64(z - t) / Float64(a - t))) + Float64(x + Float64(x * Float64(Float64(t - z) / 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)
	tmp = 0.0;
	if ((t <= -1.05e+171) || ~((t <= 1e+167)))
		tmp = ((y - x) * (a / (t / (a / t)))) + ((y + ((x - y) / (t / (z - a)))) - (a / ((t / (z / t)) / (y - x))));
	else
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (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_] := If[Or[LessEqual[t, -1.05e+171], N[Not[LessEqual[t, 1e+167]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * N[(a / N[(t / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(t / N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + N[(x * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	38.33%
Target	14.32%
Herbie	10.02%

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

Derivation

1. Split input into 2 regimes

2. if t < -1.0500000000000001e171 or 1e167 < t

   1. Initial program 75.51

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

   2. Simplified 43.32

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

      [Start] 75.51	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 75.51	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*l/ [<=] 43.45	\[ \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]
      fma-def [=>] 43.32	\[ \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Taylor expanded in t around -inf 49.12

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}} + \left(y + \left(-1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t} + \frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}}\right)\right)} \]

   4. Simplified 13.31

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

      [Start] 49.12	\[ -1 \cdot \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}} + \left(y + \left(-1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t} + \frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}}\right)\right) \]
      +-commutative [=>] 49.12	\[ \color{blue}{\left(y + \left(-1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t} + \frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}}\right)\right) + -1 \cdot \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}}} \]
      mul-1-neg [=>] 49.12	\[ \left(y + \left(-1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t} + \frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}}\right)\right) + \color{blue}{\left(-\frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}}\right)} \]
      unsub-neg [=>] 49.12	\[ \color{blue}{\left(y + \left(-1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t} + \frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}}\right)\right) - \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}}} \]
      associate-+r+ [=>] 49.12	\[ \color{blue}{\left(\left(y + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t}\right) + \frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}}\right)} - \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}} \]
      +-commutative [=>] 49.12	\[ \color{blue}{\left(\frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}} + \left(y + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t}\right)\right)} - \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}} \]
      associate--l+ [=>] 49.12	\[ \color{blue}{\frac{{a}^{2} \cdot \left(y - x\right)}{{t}^{2}} + \left(\left(y + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t}\right) - \frac{a \cdot \left(\left(y - x\right) \cdot z\right)}{{t}^{2}}\right)} \]

   if -1.0500000000000001e171 < t < 1e167

   1. Initial program 25.26

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

   2. Simplified 12.22

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

      [Start] 25.26	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 12.22	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Applied egg-rr 8.87

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t} - \left(x \cdot \frac{z - t}{a - t} - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 10.02

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+171} \lor \neg \left(t \leq 10^{+167}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{a}{\frac{t}{\frac{a}{t}}} + \left(\left(y + \frac{x - y}{\frac{t}{z - a}}\right) - \frac{a}{\frac{\frac{t}{\frac{z}{t}}}{y - x}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + \left(x + x \cdot \frac{t - z}{a - t}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	11.53%
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+298}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-230}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 2
Error	10.08%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+170} \lor \neg \left(t \leq 3.6 \cdot 10^{+166}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + \left(x + x \cdot \frac{t - z}{a - t}\right)\\ \end{array} \]

Alternative 3
Error	40.67%
Cost	1500

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -25.5:\\ \;\;\;\;y + \frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-124}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	37.63%
Cost	1500

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -27:\\ \;\;\;\;y + \frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-124}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 225:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	66.38%
Cost	1376

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+247}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq -2100000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-248}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-116}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 680000000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	39.5%
Cost	1236

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -26:\\ \;\;\;\;y + \frac{x \cdot z}{t}\\ \mathbf{elif}\;a \leq 440000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	27.77%
Cost	1233

\[\begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+47} \lor \neg \left(a \leq 3200\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 8
Error	24.99%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	24.41%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+41}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	31.59%
Cost	1105

\[\begin{array}{l} t_1 := x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{+47} \lor \neg \left(a \leq 2600\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 11
Error	29.99%
Cost	1104

\[\begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -3.45 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+63}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	15.2%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+158} \lor \neg \left(t \leq 4.7 \cdot 10^{+166}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 13
Error	12.59%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+158} \lor \neg \left(t \leq 5.8 \cdot 10^{+167}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 14
Error	42.25%
Cost	976

\[\begin{array}{l} t_1 := y + \frac{x \cdot z}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-237}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 0.38:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	41.11%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+47} \lor \neg \left(a \leq 5.5\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot z}{t}\\ \end{array} \]

Alternative 16
Error	46.54%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+173}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17
Error	54.96%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 370000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	70.77%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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))))