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

Average Error: 24.9 → 6.2

Time: 35.0s

Precision: binary64

Cost: 3208

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \frac{t - z}{t - a} + \left(x + \left(-\left(t - z\right) \cdot \frac{x}{t - a}\right)\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + -1 \cdot \left(\left(y - x\right) \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (+ (* y (/ (- t z) (- t a))) (+ x (- (* (- t z) (/ x (- t a)))))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-308)
     t_1
     (if (<= t_2 0.0) (+ y (* -1.0 (* (- y x) (- (/ z t) (/ a t))))) t_1))))

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 = (y * ((t - z) / (t - a))) + (x + -((t - z) * (x / (t - a))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-308) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (-1.0 * ((y - x) * ((z / t) - (a / t))));
	} else {
		tmp = t_1;
	}
	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 = (y * ((t - z) / (t - a))) + (x + -((t - z) * (x / (t - a))))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-5d-308)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = y + ((-1.0d0) * ((y - x) * ((z / t) - (a / t))))
    else
        tmp = t_1
    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 = (y * ((t - z) / (t - a))) + (x + -((t - z) * (x / (t - a))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-308) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (-1.0 * ((y - x) * ((z / t) - (a / t))));
	} else {
		tmp = t_1;
	}
	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 = (y * ((t - z) / (t - a))) + (x + -((t - z) * (x / (t - a))))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -5e-308:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = y + (-1.0 * ((y - x) * ((z / t) - (a / t))))
	else:
		tmp = t_1
	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(Float64(y * Float64(Float64(t - z) / Float64(t - a))) + Float64(x + Float64(-Float64(Float64(t - z) * Float64(x / Float64(t - a))))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-308)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(-1.0 * Float64(Float64(y - x) * Float64(Float64(z / t) - Float64(a / t)))));
	else
		tmp = t_1;
	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 = (y * ((t - z) / (t - a))) + (x + -((t - z) * (x / (t - a))));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -5e-308)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = y + (-1.0 * ((y - x) * ((z / t) - (a / t))));
	else
		tmp = t_1;
	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[(N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + (-N[(N[(t - z), $MachinePrecision] * N[(x / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-308], t$95$1, If[LessEqual[t$95$2, 0.0], N[(y + N[(-1.0 * N[(N[(y - x), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Target

Original	24.9
Target	9.2
Herbie	6.2

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999955e-308 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 21.6

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

   2. Simplified 10.3

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

      [Start] 21.6	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      rational.json-simplify-49 [=>] 10.3	\[ x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   3. Applied egg-rr 7.2

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

   4. Taylor expanded in y around -inf 21.6

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

   5. Simplified 6.7

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

      [Start] 21.6	\[ -1 \cdot \frac{\left(t - z\right) \cdot x}{t - a} + \left(\frac{y \cdot \left(t - z\right)}{t - a} + x\right) \]
      rational.json-simplify-41 [=>] 21.4	\[ \color{blue}{\frac{y \cdot \left(t - z\right)}{t - a} + \left(x + -1 \cdot \frac{\left(t - z\right) \cdot x}{t - a}\right)} \]
      rational.json-simplify-2 [=>] 21.4	\[ \frac{\color{blue}{\left(t - z\right) \cdot y}}{t - a} + \left(x + -1 \cdot \frac{\left(t - z\right) \cdot x}{t - a}\right) \]
      rational.json-simplify-49 [=>] 13.9	\[ \color{blue}{y \cdot \frac{t - z}{t - a}} + \left(x + -1 \cdot \frac{\left(t - z\right) \cdot x}{t - a}\right) \]
      rational.json-simplify-2 [=>] 13.9	\[ y \cdot \frac{t - z}{t - a} + \left(x + \color{blue}{\frac{\left(t - z\right) \cdot x}{t - a} \cdot -1}\right) \]
      rational.json-simplify-9 [=>] 13.9	\[ y \cdot \frac{t - z}{t - a} + \left(x + \color{blue}{\left(-\frac{\left(t - z\right) \cdot x}{t - a}\right)}\right) \]
      rational.json-simplify-2 [=>] 13.9	\[ y \cdot \frac{t - z}{t - a} + \left(x + \left(-\frac{\color{blue}{x \cdot \left(t - z\right)}}{t - a}\right)\right) \]
      rational.json-simplify-49 [=>] 6.7	\[ y \cdot \frac{t - z}{t - a} + \left(x + \left(-\color{blue}{\left(t - z\right) \cdot \frac{x}{t - a}}\right)\right) \]

   if -4.99999999999999955e-308 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 61.2

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

   2. Simplified 61.2

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

      [Start] 61.2	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      rational.json-simplify-2 [=>] 61.2	\[ x + \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} \]
      rational.json-simplify-49 [=>] 61.2	\[ x + \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} \]

   3. Taylor expanded in t around inf 0.4

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

   4. Simplified 0.4

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

      [Start] 0.4	\[ \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      rational.json-simplify-48 [=>] 0.4	\[ \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]
      rational.json-simplify-2 [=>] 0.4	\[ y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - \color{blue}{\frac{a \cdot \left(y - x\right)}{t} \cdot -1}\right) \]
      rational.json-simplify-52 [=>] 0.4	\[ y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]
      rational.json-simplify-49 [=>] 0.3	\[ y + -1 \cdot \left(\color{blue}{\left(y - x\right) \cdot \frac{z}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]
      rational.json-simplify-49 [=>] 0.4	\[ y + -1 \cdot \left(\left(y - x\right) \cdot \frac{z}{t} - \color{blue}{\left(y - x\right) \cdot \frac{a}{t}}\right) \]
      rational.json-simplify-2 [=>] 0.4	\[ y + -1 \cdot \left(\left(y - x\right) \cdot \frac{z}{t} - \color{blue}{\frac{a}{t} \cdot \left(y - x\right)}\right) \]
      rational.json-simplify-52 [=>] 0.4	\[ y + -1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\right)} \]

3. Recombined 2 regimes into one program.

4. Final simplification 6.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a} + \left(x + \left(-\left(t - z\right) \cdot \frac{x}{t - a}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + -1 \cdot \left(\left(y - x\right) \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a} + \left(x + \left(-\left(t - z\right) \cdot \frac{x}{t - a}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	6.6
Cost	2760

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + -1 \cdot \left(\left(y - x\right) \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t - z}}\\ \end{array} \]

Alternative 2
Error	7.1
Cost	2632

\[\begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \left(-\left(z - a\right) \cdot \frac{y - x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	7.1
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \left(-\left(z - a\right) \cdot \frac{y - x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t - z}}\\ \end{array} \]

Alternative 4
Error	6.6
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t - z}}\\ \end{array} \]

Alternative 5
Error	20.2
Cost	1760

\[\begin{array}{l} t_1 := x + \left(x - y\right) \cdot \frac{z}{t - a}\\ t_2 := x + \frac{t}{t - a} \cdot \left(y - x\right)\\ t_3 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+228}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+151}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z - t}{t}\right)\\ \end{array} \]

Alternative 6
Error	20.8
Cost	1760

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := x + \left(x - y\right) \cdot \frac{z}{t - a}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+229}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{t}{t - a} \cdot \left(y - x\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{+204}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z - t}{t}\right)\\ \end{array} \]

Alternative 7
Error	25.1
Cost	1628

\[\begin{array}{l} t_1 := x + \left(x - y\right) \cdot \frac{z}{t - a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq -13:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-169}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-232}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-180}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{t - z}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	34.8
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{t - a} \cdot y\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	26.6
Cost	1236

\[\begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq -95000:\\ \;\;\;\;x + \frac{z}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-168}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-233}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+71}:\\ \;\;\;\;\frac{t - z}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 10
Error	17.7
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-49}:\\ \;\;\;\;y + \left(-\left(z - a\right) \cdot \frac{y - x}{t}\right)\\ \mathbf{elif}\;a \leq 550:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;\frac{t - z}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	17.1
Cost	1228

\[\begin{array}{l} t_1 := x + \frac{z - t}{a} \cdot \left(y - x\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.58 \cdot 10^{-49}:\\ \;\;\;\;y + \left(-\left(z - a\right) \cdot \frac{y - x}{t}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+71}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	34.5
Cost	1172

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+215}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-\frac{z - t}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	34.4
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+215}:\\ \;\;\;\;\frac{t}{t - a} \cdot y\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{z - t}{a} \cdot y\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	34.4
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\frac{z - t}{a} \cdot y\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+71}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	34.5
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+254}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+215}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	26.2
Cost	972

\[\begin{array}{l} t_1 := x + \frac{z}{a} \cdot \left(y - x\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq -0.08:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	26.2
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq -850000:\\ \;\;\;\;x + \frac{z}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 18
Error	26.2
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+198}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq -10000:\\ \;\;\;\;x + \frac{z}{a} \cdot \left(y - x\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{t - z}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 19
Error	36.5
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -42000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-170}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+71}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	28.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(-\frac{t}{a}\right)\\ \end{array} \]

Alternative 21
Error	30.9
Cost	776

\[\begin{array}{l} t_1 := x + y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-\frac{z - t}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	30.9
Cost	776

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-\frac{z - t}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(-\frac{t}{a}\right)\\ \end{array} \]

Alternative 23
Error	33.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	36.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -58000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+71}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25
Error	45.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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))))