Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Average Error: 10.9 → 0.5

Time: 11.0s

Precision: binary64

Cost: 2376

Math

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

↓

\[\begin{array}{l} t_1 := \frac{a - z}{t}\\ t_2 := x + \left(\frac{y}{t_1} - \frac{z}{t_1}\right)\\ t_3 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 6 \cdot 10^{+243}:\\ \;\;\;\;t_3 + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a z) t))
        (t_2 (+ x (- (/ y t_1) (/ z t_1))))
        (t_3 (/ (* (- y z) t) (- a z))))
   (if (<= t_3 -5e+298) t_2 (if (<= t_3 6e+243) (+ t_3 x) t_2))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - z) / t;
	double t_2 = x + ((y / t_1) - (z / t_1));
	double t_3 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_3 <= -5e+298) {
		tmp = t_2;
	} else if (t_3 <= 6e+243) {
		tmp = t_3 + x;
	} else {
		tmp = t_2;
	}
	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) / (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) :: t_3
    real(8) :: tmp
    t_1 = (a - z) / t
    t_2 = x + ((y / t_1) - (z / t_1))
    t_3 = ((y - z) * t) / (a - z)
    if (t_3 <= (-5d+298)) then
        tmp = t_2
    else if (t_3 <= 6d+243) then
        tmp = t_3 + x
    else
        tmp = t_2
    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) / (a - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - z) / t;
	double t_2 = x + ((y / t_1) - (z / t_1));
	double t_3 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_3 <= -5e+298) {
		tmp = t_2;
	} else if (t_3 <= 6e+243) {
		tmp = t_3 + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = (a - z) / t
	t_2 = x + ((y / t_1) - (z / t_1))
	t_3 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_3 <= -5e+298:
		tmp = t_2
	elif t_3 <= 6e+243:
		tmp = t_3 + x
	else:
		tmp = t_2
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - z) / t)
	t_2 = Float64(x + Float64(Float64(y / t_1) - Float64(z / t_1)))
	t_3 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_3 <= -5e+298)
		tmp = t_2;
	elseif (t_3 <= 6e+243)
		tmp = Float64(t_3 + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a - z) / t;
	t_2 = x + ((y / t_1) - (z / t_1));
	t_3 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_3 <= -5e+298)
		tmp = t_2;
	elseif (t_3 <= 6e+243)
		tmp = t_3 + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y / t$95$1), $MachinePrecision] - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+298], t$95$2, If[LessEqual[t$95$3, 6e+243], N[(t$95$3 + x), $MachinePrecision], t$95$2]]]]]

Target

Original	10.9
Target	0.6
Herbie	0.5

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -5.0000000000000003e298 or 5.99999999999999969e243 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 58.4

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

   2. Applied egg-rr 1.7

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

   if -5.0000000000000003e298 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.99999999999999969e243

   1. Initial program 0.3

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -5 \cdot 10^{+298}:\\ \;\;\;\;x + \left(\frac{y}{\frac{a - z}{t}} - \frac{z}{\frac{a - z}{t}}\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 6 \cdot 10^{+243}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{a - z}{t}} - \frac{z}{\frac{a - z}{t}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	3.4
Cost	1992

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t_1 \leq 10^{+244}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{z}{t}}\\ \end{array} \]

Alternative 2
Error	2.4
Cost	1992

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+244}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{z}{t}}\\ \end{array} \]

Alternative 3
Error	25.0
Cost	1240

\[\begin{array}{l} t_1 := \frac{y}{\frac{a - z}{t}}\\ \mathbf{if}\;x \leq -3.632275279424997 \cdot 10^{-31}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq -1.5817055234956398 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2491203280262998 \cdot 10^{-183}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 7.749364167339441 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9251313622029.393:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 3.7829877897964785 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	19.4
Cost	1240

\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ t_2 := x - \frac{y \cdot t}{z}\\ \mathbf{if}\;z \leq -2.808868850083143 \cdot 10^{-8}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.4537157758165616 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-230}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.2110648219911614 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.536315587026295 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 5
Error	20.9
Cost	1108

\[\begin{array}{l} t_1 := x - \frac{y \cdot t}{z}\\ \mathbf{if}\;z \leq -2.808868850083143 \cdot 10^{-8}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-230}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.2153459185548576 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.536315587026295 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 6
Error	12.1
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4537157758165616 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.9889007285943366 \cdot 10^{-28}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(x - \frac{t}{\frac{z}{y - a}}\right)\\ \end{array} \]

Alternative 7
Error	14.6
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -39.86208699718609:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.2153459185548576 \cdot 10^{-92}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8.536315587026295 \cdot 10^{+68}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 8
Error	12.7
Cost	840

\[\begin{array}{l} t_1 := x + \frac{z - y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -1.4537157758165616 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.216223079585761 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	12.0
Cost	840

\[\begin{array}{l} t_1 := x + \frac{z - y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -1.4537157758165616 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9889007285943366 \cdot 10^{-28}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	12.0
Cost	840

\[\begin{array}{l} t_1 := x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -1.4537157758165616 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9889007285943366 \cdot 10^{-28}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	19.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -370254773158145.9:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 0.3888693910278906:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 12
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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