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

Average Error: 24.6 → 8.1

Time: 23.7s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+264}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_1 \leq 10^{+283}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]

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 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -2e+264)
     (+ x (* (- z t) (/ (- y x) (- a t))))
     (if (<= t_1 -1e-265)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (- x y) (/ t (- z a))))
         (if (<= t_1 1e+283) t_1 (+ y (* (- z a) (/ (- x y) 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 t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e+264) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else if (t_1 <= -1e-265) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (t_1 <= 1e+283) {
		tmp = t_1;
	} else {
		tmp = y + ((z - a) * ((x - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if (t_1 <= (-2d+264)) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else if (t_1 <= (-1d-265)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = y + ((x - y) / (t / (z - a)))
    else if (t_1 <= 1d+283) then
        tmp = t_1
    else
        tmp = y + ((z - a) * ((x - y) / 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 t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e+264) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else if (t_1 <= -1e-265) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (t_1 <= 1e+283) {
		tmp = t_1;
	} else {
		tmp = y + ((z - a) * ((x - y) / 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):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e+264:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	elif t_1 <= -1e-265:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + ((x - y) / (t / (z - a)))
	elif t_1 <= 1e+283:
		tmp = t_1
	else:
		tmp = y + ((z - a) * ((x - y) / 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)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e+264)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t_1 <= -1e-265)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	elseif (t_1 <= 1e+283)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / 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)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e+264)
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	elseif (t_1 <= -1e-265)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + ((x - y) / (t / (z - a)));
	elseif (t_1 <= 1e+283)
		tmp = t_1;
	else
		tmp = y + ((z - a) * ((x - y) / 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_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+264], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-265], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+283], t$95$1, N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	24.6
Target	9.2
Herbie	8.1

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

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000009e264

   1. Initial program 57.6

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

   2. Simplified 18.1

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

      [Start] 57.6	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-*l/ [<=] 18.1	\[ x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   if -2.00000000000000009e264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999985e-266 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.99999999999999955e282

   1. Initial program 2.1

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

   if -9.99999999999999985e-266 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 57.8

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

   2. Simplified 57.7

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

      [Start] 57.8	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 57.7	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Taylor expanded in t around inf 3.5

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

   4. Simplified 3.4

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

      [Start] 3.5	\[ \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      +-commutative [=>] 3.5	\[ \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right)} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      associate--l+ [=>] 3.5	\[ \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]
      *-commutative [=>] 3.5	\[ y + \left(-1 \cdot \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 3.5	\[ y + \left(\color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 3.5	\[ y + \left(\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]
      div-sub [<=] 3.5	\[ y + \color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]
      distribute-lft-out-- [=>] 3.5	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]
      associate-*r/ [<=] 3.5	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
      mul-1-neg [=>] 3.5	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]
      unsub-neg [=>] 3.5	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]
      *-commutative [<=] 3.5	\[ y - \frac{\color{blue}{z \cdot \left(y - x\right)} - a \cdot \left(y - x\right)}{t} \]
      distribute-rgt-out-- [=>] 3.5	\[ y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]
      associate-/l* [=>] 3.4	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   if 9.99999999999999955e282 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 59.0

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

   2. Simplified 15.5

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

      [Start] 59.0	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 59.0	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 15.5	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 15.5	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 15.5	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 42.1

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

   4. Simplified 23.7

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

      [Start] 42.1	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 42.1	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 42.1	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 42.1	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 42.1	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 42.1	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 42.1	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 23.8	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]
      associate-/r/ [=>] 23.7	\[ y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 8.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{+264}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+283}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]

Alternatives

Alternative 1
Error	8.0
Cost	8004

\[\begin{array}{l} t_1 := \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_2 \leq 10^{+283}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(y + t_1\right) + \frac{a}{t} \cdot t_1\\ \end{array} \]

Alternative 2
Error	7.9
Cost	4300

\[\begin{array}{l} t_1 := \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_2 \leq 10^{+283}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(y + t_1\right) + \frac{a}{t} \cdot t_1\\ \end{array} \]

Alternative 3
Error	8.0
Cost	3532

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_1 \leq 10^{+283}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 4
Error	10.6
Cost	1624

\[\begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+105}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+170}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	35.8
Cost	1568

\[\begin{array}{l} t_1 := \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-191}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-285}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+136}:\\ \;\;\;\;\frac{-y}{\frac{a - t}{t}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	35.7
Cost	1504

\[\begin{array}{l} t_1 := y \cdot \frac{t}{t - a}\\ t_2 := \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-191}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-280}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	30.6
Cost	1368

\[\begin{array}{l} t_1 := z \cdot \frac{-x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+205}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	28.5
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-20}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	24.6
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-21}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	20.4
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-12}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	34.0
Cost	1304

\[\begin{array}{l} t_1 := \frac{-y}{\frac{t}{z - t}}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	18.8
Cost	1232

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{x - y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-10}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+117}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 13
Error	20.9
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	20.1
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-13}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	19.8
Cost	1100

\[\begin{array}{l} t_1 := x + \frac{x - y}{\frac{a}{t} + -1}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	34.9
Cost	976

\[\begin{array}{l} t_1 := y \cdot \frac{t}{t - a}\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	36.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	36.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	36.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	45.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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))))