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

Average Error: 25.0 → 7.2

Time: 36.9s

Precision: binary64

Cost: 2892

Math

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

↓

\[\begin{array}{l} t_1 := x + \begin{array}{l} \mathbf{if}\;z - y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \end{array}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(a - y\right) \cdot x}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
          (if (!= (- z y) 0.0)
            (/ (- t x) (/ (- a z) (- y z)))
            (/ (* (- y z) (- x t)) (- z a)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -2e-301)
     t_1
     (if (<= t_2 0.0) (+ (- (/ (* (- a y) x) z)) t) 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 tmp;
	if ((z - y) != 0.0) {
		tmp = (t - x) / ((a - z) / (y - z));
	} else {
		tmp = ((y - z) * (x - t)) / (z - a);
	}
	double t_1 = x + tmp;
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp_1;
	if (t_2 <= -2e-301) {
		tmp_1 = t_1;
	} else if (t_2 <= 0.0) {
		tmp_1 = -(((a - y) * x) / z) + t;
	} else {
		tmp_1 = t_1;
	}
	return tmp_1;
}

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
    real(8) :: tmp_1
    if ((z - y) /= 0.0d0) then
        tmp = (t - x) / ((a - z) / (y - z))
    else
        tmp = ((y - z) * (x - t)) / (z - a)
    end if
    t_1 = x + tmp
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-2d-301)) then
        tmp_1 = t_1
    else if (t_2 <= 0.0d0) then
        tmp_1 = -(((a - y) * x) / z) + t
    else
        tmp_1 = t_1
    end if
    code = tmp_1
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 - y) != 0.0) {
		tmp = (t - x) / ((a - z) / (y - z));
	} else {
		tmp = ((y - z) * (x - t)) / (z - a);
	}
	double t_1 = x + tmp;
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp_1;
	if (t_2 <= -2e-301) {
		tmp_1 = t_1;
	} else if (t_2 <= 0.0) {
		tmp_1 = -(((a - y) * x) / z) + t;
	} else {
		tmp_1 = t_1;
	}
	return tmp_1;
}

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 - y) != 0.0:
		tmp = (t - x) / ((a - z) / (y - z))
	else:
		tmp = ((y - z) * (x - t)) / (z - a)
	t_1 = x + tmp
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp_1 = 0
	if t_2 <= -2e-301:
		tmp_1 = t_1
	elif t_2 <= 0.0:
		tmp_1 = -(((a - y) * x) / z) + t
	else:
		tmp_1 = t_1
	return tmp_1

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 (Float64(z - y) != 0.0)
		tmp = Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a));
	end
	t_1 = Float64(x + tmp)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp_1 = 0.0
	if (t_2 <= -2e-301)
		tmp_1 = t_1;
	elseif (t_2 <= 0.0)
		tmp_1 = Float64(Float64(-Float64(Float64(Float64(a - y) * x) / z)) + t);
	else
		tmp_1 = t_1;
	end
	return tmp_1
end

MATLAB

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

↓

function tmp_3 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - y) ~= 0.0)
		tmp = (t - x) / ((a - z) / (y - z));
	else
		tmp = ((y - z) * (x - t)) / (z - a);
	end
	t_1 = x + tmp;
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp_2 = 0.0;
	if (t_2 <= -2e-301)
		tmp_2 = t_1;
	elseif (t_2 <= 0.0)
		tmp_2 = -(((a - y) * x) / z) + t;
	else
		tmp_2 = t_1;
	end
	tmp_3 = tmp_2;
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 + If[Unequal[N[(z - y), $MachinePrecision], 0.0], N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-301], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(a - y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], t$95$1]]]]

Target

Original	25.0
Target	12.1
Herbie	7.2

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000013e-301 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 22.0

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

   2. Applied egg-rr 7.7

      \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z - y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ } \end{array}} \]

   if -2.00000000000000013e-301 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 60.3

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

   2. Taylor expanded in z around -inf 1.1

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

   3. Simplified 1.1

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

   4. Taylor expanded in t around 0 1.1

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

   5. Simplified 1.1

      \[\leadsto \left(-\frac{\color{blue}{\left(a - y\right) \cdot x}}{z}\right) + t \]
      Proof
3. Recombined 2 regimes into one program.

Alternatives

Alternative 1
Error	7.2
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(-\frac{\left(a - y\right) \cdot x}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	17.9
Cost	1560

\[\begin{array}{l} t_1 := x + \frac{y - z}{a} \cdot \left(t - x\right)\\ t_2 := \left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ \mathbf{if}\;z \leq -3 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	18.5
Cost	1296

\[\begin{array}{l} t_1 := \left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ t_2 := x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 75:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	18.1
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;\left(-\frac{\left(a - y\right) \cdot x}{z}\right) + t\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 660:\\ \;\;\;\;t - \begin{array}{l} \mathbf{if}\;y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{z}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	18.0
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{+47}:\\ \;\;\;\;\left(-\frac{\left(a - y\right) \cdot x}{z}\right) + t\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.4:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	18.2
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+47}:\\ \;\;\;\;\left(-\frac{\left(a - y\right) \cdot x}{z}\right) + t\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 5:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	20.8
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;\left(-\frac{\left(a - y\right) \cdot x}{z}\right) + t\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 45000:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	12.6
Cost	1096

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-63}:\\ \;\;\;\;\left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	24.5
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 180:\\ \;\;\;\;t - \left(-\frac{y \cdot x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.1
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 245:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	31.0
Cost	776

\[\begin{array}{l} t_1 := x + \left(-\frac{y}{a}\right) \cdot x\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9500:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	29.6
Cost	776

\[\begin{array}{l} t_1 := x + \left(-\frac{y}{a}\right) \cdot x\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;t - \left(-\frac{y \cdot x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	33.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 135:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	36.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	46.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023010 
(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))))