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

Average Error: 24.9 → 7.7

Time: 26.8s

Precision: binary64

Cost: 3661

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - x\right)\\ t_2 := x + \frac{t_1}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2 \cdot 10^{+284}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{t_1}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t x))) (t_2 (+ x (/ t_1 (- a z)))))
   (if (<= t_2 -2e-296)
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (if (or (<= t_2 0.0) (not (<= t_2 2e+284)))
       (+ t (* (- t x) (/ (- a y) z)))
       (+ x (/ 1.0 (/ (- a z) t_1)))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t - x);
	double t_2 = x + (t_1 / (a - z));
	double tmp;
	if (t_2 <= -2e-296) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+284)) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + (1.0 / ((a - z) / 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 - z) * (t - x)) / (a - z))
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 - z) * (t - x)
    t_2 = x + (t_1 / (a - z))
    if (t_2 <= (-2d-296)) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2d+284))) then
        tmp = t + ((t - x) * ((a - y) / z))
    else
        tmp = x + (1.0d0 / ((a - z) / 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 - z) * (t - x)) / (a - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t - x);
	double t_2 = x + (t_1 / (a - z));
	double tmp;
	if (t_2 <= -2e-296) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+284)) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + (1.0 / ((a - z) / t_1));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = (y - z) * (t - x)
	t_2 = x + (t_1 / (a - z))
	tmp = 0
	if t_2 <= -2e-296:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	elif (t_2 <= 0.0) or not (t_2 <= 2e+284):
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = x + (1.0 / ((a - z) / t_1))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t - x))
	t_2 = Float64(x + Float64(t_1 / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-296)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	elseif ((t_2 <= 0.0) || !(t_2 <= 2e+284))
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(1.0 / Float64(Float64(a - z) / t_1)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t - x);
	t_2 = x + (t_1 / (a - z));
	tmp = 0.0;
	if (t_2 <= -2e-296)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	elseif ((t_2 <= 0.0) || ~((t_2 <= 2e+284)))
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = x + (1.0 / ((a - z) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-296], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2e+284]], $MachinePrecision]], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(N[(a - z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	24.9
Target	11.8
Herbie	7.7

\[\begin{array}{l} \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-296

   1. Initial program 22.6

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

   2. Simplified 7.8

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

      [Start] 22.6	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 7.8	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   if -2e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0 or 2.00000000000000016e284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 60.1

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

   2. Simplified 32.8

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

      [Start] 60.1	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 60.1	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 32.8	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 32.8	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Taylor expanded in z around inf 26.4

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

   4. Simplified 15.0

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

      [Start] 26.4	\[ \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 26.4	\[ \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]
      distribute-lft-out-- [=>] 26.4	\[ t + \frac{\color{blue}{\left(-1 \cdot \left(y - a\right)\right)} \cdot \left(t - x\right)}{z} \]
      associate-*r* [<=] 26.4	\[ t + \frac{\color{blue}{-1 \cdot \left(\left(y - a\right) \cdot \left(t - x\right)\right)}}{z} \]
      mul-1-neg [=>] 26.4	\[ t + \frac{\color{blue}{-\left(y - a\right) \cdot \left(t - x\right)}}{z} \]
      distribute-neg-frac [<=] 26.4	\[ t + \color{blue}{\left(-\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 26.4	\[ \color{blue}{t - \frac{\left(y - a\right) \cdot \left(t - x\right)}{z}} \]
      associate-*l/ [<=] 15.0	\[ t - \color{blue}{\frac{y - a}{z} \cdot \left(t - x\right)} \]

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000016e284

   1. Initial program 1.9

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

   2. Simplified 2.6

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

      [Start] 1.9	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 2.6	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Applied egg-rr 2.0

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 7.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0 \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+284}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Error	7.7
Cost	3533

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t_1 \leq 0 \lor \neg \left(t_1 \leq 2 \cdot 10^{+284}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	24.0
Cost	1501

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+25}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+16} \lor \neg \left(z \leq 2.05 \cdot 10^{+49}\right) \land z \leq 2.1 \cdot 10^{+161}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	24.2
Cost	1501

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+25}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-89}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-39}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 175000 \lor \neg \left(z \leq 3.9 \cdot 10^{+50}\right) \land z \leq 7.9 \cdot 10^{+161}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 4
Error	20.5
Cost	1500

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a - z}{z}}\\ t_2 := t - \frac{x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-89}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-46}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 195000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	20.4
Cost	1500

\[\begin{array}{l} t_1 := t - \frac{x}{z} \cdot \left(a - y\right)\\ t_2 := x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-89}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{t - x}}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-53}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	18.2
Cost	1496

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a - z}{z}}\\ t_2 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{t - x}}{y}}\\ \mathbf{elif}\;z \leq 10^{-39}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	17.8
Cost	1496

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a - z}{z}}\\ t_2 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{t - x}}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-52}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	17.8
Cost	1496

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{t - x}}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-52}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3800000000:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	32.3
Cost	1436

\[\begin{array}{l} t_1 := \left(-t\right) \cdot \frac{z}{a - z}\\ t_2 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-167}:\\ \;\;\;\;\frac{z}{\frac{z - a}{t}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10
Error	37.6
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-222}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + t \cdot \frac{a}{z}\\ \end{array} \]

Alternative 11
Error	37.7
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-230}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	22.0
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	8.8
Cost	1097

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+60} \lor \neg \left(z \leq 2.05 \cdot 10^{+224}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 14
Error	36.8
Cost	976

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-167}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	24.6
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+131} \lor \neg \left(a \leq 2.3 \cdot 10^{+112}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 16
Error	23.5
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+131} \lor \neg \left(a \leq 1.6 \cdot 10^{+110}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17
Error	27.6
Cost	777

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+42} \lor \neg \left(z \leq 3.4 \cdot 10^{+69}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18
Error	36.1
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	36.2
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	26.6
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+41} \lor \neg \left(z \leq 5.8 \cdot 10^{+69}\right):\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 21
Error	26.6
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+41} \lor \neg \left(z \leq 4.7 \cdot 10^{+70}\right):\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 22
Error	29.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + t \cdot \frac{a}{z}\\ \end{array} \]

Alternative 23
Error	35.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24
Error	45.7
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023031 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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