Development.Shake.Progress:decay from shake-0.15.5

Average Error: 23.5 → 10.1

Time: 22.1s

Precision: binary64

Cost: 1476

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.788675350393175:\\ \;\;\;\;t_1 + \frac{-1}{z} \cdot \left(x + \frac{a - t}{b - y}\right)\\ \mathbf{elif}\;z \leq 171086553456.3898:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4.788675350393175)
     (+ t_1 (* (/ -1.0 z) (+ x (/ (- a t) (- b y)))))
     (if (<= z 171086553456.3898)
       (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))
       (- t_1 (/ x z))))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.788675350393175) {
		tmp = t_1 + ((-1.0 / z) * (x + ((a - t) / (b - y))));
	} else if (z <= 171086553456.3898) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	} else {
		tmp = t_1 - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

↓

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-4.788675350393175d0)) then
        tmp = t_1 + (((-1.0d0) / z) * (x + ((a - t) / (b - y))))
    else if (z <= 171086553456.3898d0) then
        tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
    else
        tmp = t_1 - (x / z)
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.788675350393175) {
		tmp = t_1 + ((-1.0 / z) * (x + ((a - t) / (b - y))));
	} else if (z <= 171086553456.3898) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	} else {
		tmp = t_1 - (x / z);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.788675350393175:
		tmp = t_1 + ((-1.0 / z) * (x + ((a - t) / (b - y))))
	elif z <= 171086553456.3898:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
	else:
		tmp = t_1 - (x / z)
	return tmp

Julia

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

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.788675350393175)
		tmp = Float64(t_1 + Float64(Float64(-1.0 / z) * Float64(x + Float64(Float64(a - t) / Float64(b - y)))));
	elseif (z <= 171086553456.3898)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	else
		tmp = Float64(t_1 - Float64(x / z));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.788675350393175)
		tmp = t_1 + ((-1.0 / z) * (x + ((a - t) / (b - y))));
	elseif (z <= 171086553456.3898)
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	else
		tmp = t_1 - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.788675350393175], N[(t$95$1 + N[(N[(-1.0 / z), $MachinePrecision] * N[(x + N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 171086553456.3898], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	23.5
Target	18.5
Herbie	10.1

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

Derivation

1. Split input into 3 regimes

2. if z < -4.7886753503931754

   1. Initial program 40.4

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

   2. Taylor expanded in z around inf 22.4

      \[\leadsto \color{blue}{\left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)} \]

   3. Simplified 0.6

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

   4. Applied egg-rr 1.1

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

   5. Taylor expanded in y around inf 10.3

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

   if -4.7886753503931754 < z < 171086553456.389801

   1. Initial program 9.0

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

   2. Taylor expanded in b around inf 9.9

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

   if 171086553456.389801 < z

   1. Initial program 37.9

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

   2. Taylor expanded in z around inf 22.0

      \[\leadsto \color{blue}{\left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)} \]

   3. Simplified 0.3

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

   4. Applied egg-rr 1.1

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

   5. Taylor expanded in y around inf 10.1

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} + \frac{t - a}{b - y} \]

   6. Simplified 10.1

      \[\leadsto \color{blue}{\frac{-x}{z}} + \frac{t - a}{b - y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 10.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.788675350393175:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{-1}{z} \cdot \left(x + \frac{a - t}{b - y}\right)\\ \mathbf{elif}\;z \leq 171086553456.3898:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	34.7
Cost	1636

\[\begin{array}{l} t_1 := x - \frac{z}{\frac{y}{a}}\\ t_2 := \frac{t - a}{b}\\ t_3 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.631649115207703 \cdot 10^{+237}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.8969892919253015 \cdot 10^{+144}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;z \leq -4.9244351199905184 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.788675350393175:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.342261122635375 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7545570461513878 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.446394595345878 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.701502193658882 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	18.7
Cost	1364

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -0.00010349483549088438:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0464965507409769 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 4.9784847803818075 \cdot 10^{-174}:\\ \;\;\;\;\frac{y \cdot \frac{x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 3.4024386097497606 \cdot 10^{-169}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{-t}{z + -1}\\ \mathbf{elif}\;z \leq 3861.3576663993167:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	19.0
Cost	1364

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -0.00010349483549088438:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7545570461513878 \cdot 10^{-189}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 5.009612722714174 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.6674278281406976 \cdot 10^{-29}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq 171086553456.3898:\\ \;\;\;\;\frac{y \cdot \frac{x}{z} - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	20.2
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{z \cdot t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0464965507409769 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9784847803818075 \cdot 10^{-174}:\\ \;\;\;\;\frac{y \cdot \frac{x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 8.460496179392414 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6674278281406976 \cdot 10^{-29}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	20.3
Cost	1236

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0464965507409769 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 4.9784847803818075 \cdot 10^{-174}:\\ \;\;\;\;\frac{y \cdot \frac{x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 3.4024386097497606 \cdot 10^{-169}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{-t}{z + -1}\\ \mathbf{elif}\;z \leq 1.6674278281406976 \cdot 10^{-29}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	10.0
Cost	1224

\[\begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -4.788675350393175:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 171086553456.3898:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	36.0
Cost	1112

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{t}{b - y}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -1.631649115207703 \cdot 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8969892919253015 \cdot 10^{+144}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;z \leq -4.9244351199905184 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7545570461513878 \cdot 10^{-189}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.009612722714174 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.717806170851278 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	42.2
Cost	984

\[\begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1832867436954659.8:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.0102719051407277 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 20717.86590712786:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.0331478272225832 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	24.0
Cost	976

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.9244351199905184 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7545570461513878 \cdot 10^{-189}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 8.446394595345878 \cdot 10^{-147}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 3.701502193658882 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{z}{\frac{y}{a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	21.7
Cost	976

\[\begin{array}{l} t_1 := x - \frac{a}{\frac{y}{z}}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7545570461513878 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.446394595345878 \cdot 10^{-147}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.6674278281406976 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	19.5
Cost	972

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.460496179392414 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.6674278281406976 \cdot 10^{-29}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	35.8
Cost	848

\[\begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7545570461513878 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.009612722714174 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5129286769165388 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 13
Error	20.2
Cost	844

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.237074853610584 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.6674278281406976 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.3
Cost	584

\[\begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5129286769165388 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	30.2
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.307802878646632 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.465669625109332 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	40.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3540713679207713 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.5129286769165388 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17
Error	47.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

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