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

Percentage Accurate: 80.2% → 94.8%

Time: 31.7s

Precision: binary64

Cost: 1096

• could not determine a ground truth

  1. x = 9.983727154251221e+118
  2. y = 1.334847683568321e-237
  3. z = -1.1850238862592188e+258
  4. t = -3.9174413565460496e+281
  5. a = 1.3897958145376276e+274

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{a - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e+54)
   (- x (/ (- a z) (/ t y)))
   (if (<= t 6.5e+49)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (+ (- x (/ y (/ t a))) (/ y (/ t z))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+54) {
		tmp = x - ((a - z) / (t / y));
	} else if (t <= 6.5e+49) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	}
	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) * y) / (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) :: tmp
    if (t <= (-1.35d+54)) then
        tmp = x - ((a - z) / (t / y))
    else if (t <= 6.5d+49) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = (x - (y / (t / a))) + (y / (t / z))
    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) * y) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+54) {
		tmp = x - ((a - z) / (t / y));
	} else if (t <= 6.5e+49) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e+54:
		tmp = x - ((a - z) / (t / y))
	elif t <= 6.5e+49:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = (x - (y / (t / a))) + (y / (t / z))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e+54)
		tmp = Float64(x - Float64(Float64(a - z) / Float64(t / y)));
	elseif (t <= 6.5e+49)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.35e+54)
		tmp = x - ((a - z) / (t / y));
	elseif (t <= 6.5e+49)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = (x - (y / (t / a))) + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e+54], N[(x - N[(N[(a - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+49], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	80.2%
Target	88.8%
Herbie	94.8%

\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000005e54

   1. Initial program 53.4%

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

   2. Simplified 75.0%

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

      [Start] 53.4%	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 56.8%	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      associate-/l* [=>] 75.0%	\[ x + \left(y - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\right) \]

   3. Applied egg-rr 74.9%

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

      [Start] 75.0%	\[ x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right) \]
      div-inv [=>] 75.0%	\[ x + \left(y - \color{blue}{\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}}\right) \]
      clear-num [<=] 74.9%	\[ x + \left(y - \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}}\right) \]

   4. Taylor expanded in t around inf 96.5%

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{a - z}{\frac{t}{y}}} \]
      Step-by-step derivation

      [Start] 96.5%	\[ \left(-1 \cdot \frac{y \cdot a}{t} + x\right) - -1 \cdot \frac{y \cdot z}{t} \]
      cancel-sign-sub-inv [=>] 96.5%	\[ \color{blue}{\left(-1 \cdot \frac{y \cdot a}{t} + x\right) + \left(--1\right) \cdot \frac{y \cdot z}{t}} \]
      +-commutative [=>] 96.5%	\[ \color{blue}{\left(x + -1 \cdot \frac{y \cdot a}{t}\right)} + \left(--1\right) \cdot \frac{y \cdot z}{t} \]
      metadata-eval [=>] 96.5%	\[ \left(x + -1 \cdot \frac{y \cdot a}{t}\right) + \color{blue}{1} \cdot \frac{y \cdot z}{t} \]
      *-lft-identity [=>] 96.5%	\[ \left(x + -1 \cdot \frac{y \cdot a}{t}\right) + \color{blue}{\frac{y \cdot z}{t}} \]
      associate-+l+ [=>] 96.5%	\[ \color{blue}{x + \left(-1 \cdot \frac{y \cdot a}{t} + \frac{y \cdot z}{t}\right)} \]
      *-lft-identity [<=] 96.5%	\[ x + \left(-1 \cdot \frac{y \cdot a}{t} + \color{blue}{1 \cdot \frac{y \cdot z}{t}}\right) \]
      metadata-eval [<=] 96.5%	\[ x + \left(-1 \cdot \frac{y \cdot a}{t} + \color{blue}{\left(--1\right)} \cdot \frac{y \cdot z}{t}\right) \]
      cancel-sign-sub-inv [<=] 96.5%	\[ x + \color{blue}{\left(-1 \cdot \frac{y \cdot a}{t} - -1 \cdot \frac{y \cdot z}{t}\right)} \]
      distribute-lft-out-- [=>] 96.5%	\[ x + \color{blue}{-1 \cdot \left(\frac{y \cdot a}{t} - \frac{y \cdot z}{t}\right)} \]
      div-sub [<=] 96.5%	\[ x + -1 \cdot \color{blue}{\frac{y \cdot a - y \cdot z}{t}} \]
      mul-1-neg [=>] 96.5%	\[ x + \color{blue}{\left(-\frac{y \cdot a - y \cdot z}{t}\right)} \]
      unsub-neg [=>] 96.5%	\[ \color{blue}{x - \frac{y \cdot a - y \cdot z}{t}} \]
      distribute-lft-out-- [=>] 96.5%	\[ x - \frac{\color{blue}{y \cdot \left(a - z\right)}}{t} \]
      *-commutative [=>] 96.5%	\[ x - \frac{\color{blue}{\left(a - z\right) \cdot y}}{t} \]
      sub-neg [=>] 96.5%	\[ x - \frac{\color{blue}{\left(a + \left(-z\right)\right)} \cdot y}{t} \]
      mul-1-neg [<=] 96.5%	\[ x - \frac{\left(a + \color{blue}{-1 \cdot z}\right) \cdot y}{t} \]
      +-commutative [<=] 96.5%	\[ x - \frac{\color{blue}{\left(-1 \cdot z + a\right)} \cdot y}{t} \]

   if -1.35000000000000005e54 < t < 6.5000000000000005e49

   1. Initial program 93.4%

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

   2. Simplified 96.0%

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

      [Start] 93.4%	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 93.4%	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      associate-/l* [=>] 96.0%	\[ x + \left(y - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\right) \]

   if 6.5000000000000005e49 < t

   1. Initial program 52.0%

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

   2. Simplified 74.7%

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

      [Start] 52.0%	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 56.5%	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      associate-/l* [=>] 74.7%	\[ x + \left(y - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\right) \]

   3. Taylor expanded in t around inf 89.6%

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

   4. Simplified 99.8%

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

      [Start] 89.6%	\[ \left(-1 \cdot \frac{y \cdot a}{t} + x\right) - -1 \cdot \frac{y \cdot z}{t} \]
      sub-neg [=>] 89.6%	\[ \color{blue}{\left(-1 \cdot \frac{y \cdot a}{t} + x\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right)} \]
      +-commutative [=>] 89.6%	\[ \color{blue}{\left(x + -1 \cdot \frac{y \cdot a}{t}\right)} + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      mul-1-neg [=>] 89.6%	\[ \left(x + \color{blue}{\left(-\frac{y \cdot a}{t}\right)}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      unsub-neg [=>] 89.6%	\[ \color{blue}{\left(x - \frac{y \cdot a}{t}\right)} + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      associate-/l* [=>] 89.6%	\[ \left(x - \color{blue}{\frac{y}{\frac{t}{a}}}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      mul-1-neg [=>] 89.6%	\[ \left(x - \frac{y}{\frac{t}{a}}\right) + \left(-\color{blue}{\left(-\frac{y \cdot z}{t}\right)}\right) \]
      remove-double-neg [=>] 89.6%	\[ \left(x - \frac{y}{\frac{t}{a}}\right) + \color{blue}{\frac{y \cdot z}{t}} \]
      associate-/l* [=>] 99.8%	\[ \left(x - \frac{y}{\frac{t}{a}}\right) + \color{blue}{\frac{y}{\frac{t}{z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{a - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	94.8%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{a - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 2
Accuracy	94.1%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;x + \left(y + \left(t - z\right) \cdot \frac{y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3
Accuracy	94.3%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{a - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 4
Accuracy	95.3%
Cost	1088

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

Alternative 5
Accuracy	77.0%
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;y + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -23:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Accuracy	93.3%
Cost	968

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 7
Accuracy	84.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -380000000 \lor \neg \left(t \leq 1.6 \cdot 10^{-106}\right):\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8
Accuracy	90.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-16} \lor \neg \left(a \leq 1.15 \cdot 10^{-31}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 9
Accuracy	78.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -0.48:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-32}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Accuracy	77.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -0.00064:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Accuracy	57.7%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-249}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-230}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12
Accuracy	62.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	48.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023277 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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