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

Average Error: 24.5 → 9.8

Time: 28.4s

Precision: binary64

Cost: 1096

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+104}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+104)
   (+ t (* (- y a) (/ (- x t) z)))
   (if (<= z 4.38e+20)
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (* (- t x) (/ (- a y) z))))))

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 tmp;
	if (z <= -4.4e+104) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (z <= 4.38e+20) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	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) :: tmp
    if (z <= (-4.4d+104)) then
        tmp = t + ((y - a) * ((x - t) / z))
    else if (z <= 4.38d+20) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((t - x) * ((a - y) / z))
    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 tmp;
	if (z <= -4.4e+104) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (z <= 4.38e+20) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	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):
	tmp = 0
	if z <= -4.4e+104:
		tmp = t + ((y - a) * ((x - t) / z))
	elif z <= 4.38e+20:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((t - x) * ((a - y) / z))
	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)
	tmp = 0.0
	if (z <= -4.4e+104)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	elseif (z <= 4.38e+20)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	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)
	tmp = 0.0;
	if (z <= -4.4e+104)
		tmp = t + ((y - a) * ((x - t) / z));
	elseif (z <= 4.38e+20)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((t - x) * ((a - y) / z));
	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_] := If[LessEqual[z, -4.4e+104], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.38e+20], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	24.5
Target	11.6
Herbie	9.8

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

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000001e104

   1. Initial program 44.4

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

   2. Simplified 19.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
      Proof
      (fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)) x)): 0 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))): 4 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 25.8

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

   4. Simplified 13.4

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
      Proof
      (-.f64 t (*.f64 (/.f64 (-.f64 t x) z) (-.f64 y a))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 t x) (/.f64 z (-.f64 y a))))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y a)) z))): 10 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y a) (-.f64 t x))) z)): 0 points increase in error, 2 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (*.f64 (-.f64 y a) (-.f64 t x)) z)))): 2 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (*.f64 (-.f64 y a) (-.f64 t x))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (-.f64 y a) (-.f64 t x)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 (-.f64 y a)) (-.f64 t x))) z)): 0 points increase in error, 10 points decrease in error
      (+.f64 t (/.f64 (*.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 y) (*.f64 -1 a))) (-.f64 t x)) z)): 10 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z) t)): 0 points increase in error, 2 points decrease in error

   if -4.40000000000000001e104 < z < 4.38e20

   1. Initial program 11.3

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

   2. Simplified 5.7

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
      Proof
      (fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)) x)): 0 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))): 4 points increase in error, 0 points decrease in error

   if 4.38e20 < z

   1. Initial program 38.3

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

   2. Simplified 18.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
      Proof
      (fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)) x)): 0 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))): 4 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 26.7

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

   4. Simplified 15.9

      \[\leadsto \color{blue}{t - \frac{y - a}{z} \cdot \left(t - x\right)} \]
      Proof
      (-.f64 t (*.f64 (/.f64 (-.f64 t x) z) (-.f64 y a))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 t x) (/.f64 z (-.f64 y a))))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y a)) z))): 10 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y a) (-.f64 t x))) z)): 0 points increase in error, 2 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (*.f64 (-.f64 y a) (-.f64 t x)) z)))): 2 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (*.f64 (-.f64 y a) (-.f64 t x))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (-.f64 y a) (-.f64 t x)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 -1 (-.f64 y a)) (-.f64 t x))) z)): 0 points increase in error, 10 points decrease in error
      (+.f64 t (/.f64 (*.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 y) (*.f64 -1 a))) (-.f64 t x)) z)): 10 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z) t)): 0 points increase in error, 2 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 9.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+104}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	43.1
Cost	1636

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z - a}\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-163}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	42.8
Cost	1636

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z - a}\\ \mathbf{if}\;y \leq -6.1 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-165}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{+108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	44.9
Cost	1508

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-167}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 4
Error	27.3
Cost	1369

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -32000:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-82} \lor \neg \left(z \leq 9 \cdot 10^{-55}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5
Error	31.4
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_3 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-38}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	26.9
Cost	1236

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+113}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-81}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 7
Error	18.1
Cost	1232

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ t_2 := t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	18.0
Cost	1232

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+47}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 78000000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]

Alternative 9
Error	36.9
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-79}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	19.8
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ t_2 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	19.9
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.46 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 12
Error	29.1
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 13
Error	37.4
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Error	23.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-54}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 15
Error	23.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 16
Error	23.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+92}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-55}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17
Error	27.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+92} \lor \neg \left(z \leq 2.55 \cdot 10^{+23}\right):\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18
Error	29.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+20}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	28.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 20
Error	36.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	45.6
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022343 
(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))))