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

Average Error: 24.7 → 6.8

Time: 33.1s

Precision: binary64

Cost: 2760

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (+ x (* (- t x) (* (- y z) (/ 1.0 (- a z))))))
        (t_2 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_2 -5e-296)
     t_1
     (if (<= t_2 0.0) (- t (/ (* (- t x) (- y 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 = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -5e-296) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} 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 - 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 = x + ((t - x) * ((y - z) * (1.0d0 / (a - z))))
    t_2 = x - (((y - z) * (x - t)) / (a - z))
    if (t_2 <= (-5d-296)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t - (((t - x) * (y - a)) / z)
    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 - z) * (t - x)) / (a - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -5e-296) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = 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 = x + ((t - x) * ((y - z) * (1.0 / (a - z))))
	t_2 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if t_2 <= -5e-296:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t - (((t - x) * (y - a)) / z)
	else:
		tmp = 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(x + Float64(Float64(t - x) * Float64(Float64(y - z) * Float64(1.0 / Float64(a - z)))))
	t_2 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-296)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = 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 = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	t_2 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -5e-296)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t - (((t - x) * (y - a)) / z);
	else
		tmp = 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[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-296], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Target

Original	24.7
Target	11.7
Herbie	6.8

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-296 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 21.5

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

   2. Applied egg-rr 7.4

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

   if -5.0000000000000003e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 60.7

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

   2. Applied egg-rr 61.1

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

   3. Taylor expanded in z around inf 1.1

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

   4. Simplified 1.1

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

4. Final simplification 6.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -5 \cdot 10^{-296}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.1
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t_2 \leq 10^{+257}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	34.4
Cost	1632

\[\begin{array}{l} t_1 := \frac{y}{\frac{z - a}{x - t}}\\ \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.777144533366083 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \end{array} \]

Alternative 3
Error	19.1
Cost	1496

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y - z}}\\ t_2 := t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -2.8228350788081454 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y - z}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2357486331973897 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	29.0
Cost	1368

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.917616744353138 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.300904323955291 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x - t}}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Error	31.3
Cost	1240

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.917616744353138 \cdot 10^{-15}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.2357486331973897 \cdot 10^{+96}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	29.8
Cost	1236

\[\begin{array}{l} \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.917616744353138 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	15.3
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -2.8228350788081454 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-120}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 4.653495852066283 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	31.1
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	25.8
Cost	1104

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -8.146763554882333 \cdot 10^{+188}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.300013867633317 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.917616744353138 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 9.3573721232676 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	24.4
Cost	1104

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -8.146763554882333 \cdot 10^{+188}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.300013867633317 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.3573721232676 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Error	23.6
Cost	1104

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -8.146763554882333 \cdot 10^{+188}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.300013867633317 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.3573721232676 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	23.7
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4383997814715265 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 + \frac{y - z}{z - a}\right)\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 13
Error	20.9
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-179}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 14
Error	18.6
Cost	1100

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 10^{-66}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	31.2
Cost	976

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.300013867633317 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.917616744353138 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2357486331973897 \cdot 10^{+96}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Error	36.4
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	23.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 18
Error	35.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.887359300654938 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	36.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.300013867633317 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	62.1
Cost	64

\[0 \]

Alternative 21
Error	45.4
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022308 
(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))))