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

Average Accuracy: 83.5% → 99.0%

Time: 13.5s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+43} \lor \neg \left(t \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+43) (not (<= t 5e-37)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ x (/ (* t (- y z)) (- a z)))))

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 tmp;
	if ((t <= -5e+43) || !(t <= 5e-37)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((t * (y - z)) / (a - 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) / (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) :: tmp
    if ((t <= (-5d+43)) .or. (.not. (t <= 5d-37))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x + ((t * (y - z)) / (a - 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) / (a - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+43) || !(t <= 5e-37)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((t * (y - z)) / (a - z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e+43) or not (t <= 5e-37):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x + ((t * (y - z)) / (a - z))
	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)
	tmp = 0.0
	if ((t <= -5e+43) || !(t <= 5e-37))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	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)
	tmp = 0.0;
	if ((t <= -5e+43) || ~((t <= 5e-37)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x + ((t * (y - z)) / (a - z));
	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_] := If[Or[LessEqual[t, -5e+43], N[Not[LessEqual[t, 5e-37]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	83.5%
Target	99.1%
Herbie	99.0%

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

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000004e43 or 4.9999999999999997e-37 < t

   1. Initial program 65.0%

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

   2. Simplified 98.9%

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

      [Start] 65.0	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 98.9	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -5.0000000000000004e43 < t < 4.9999999999999997e-37

   1. Initial program 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+43} \lor \neg \left(t \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	74.9%
Cost	1764

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := x + \frac{y}{\frac{a - z}{t}}\\ t_3 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.72 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-144}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-31}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	75.6%
Cost	1764

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{t \cdot y}{a - z}\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-255}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-145}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	76.7%
Cost	972

\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-24}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	81.2%
Cost	972

\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	67.0%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.000225:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	66.3%
Cost	844

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+200}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	78.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-38} \lor \neg \left(z \leq 3 \cdot 10^{+41}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8
Accuracy	78.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-38} \lor \neg \left(z \leq 1.45 \cdot 10^{+37}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9
Accuracy	78.6%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-38} \lor \neg \left(z \leq 7 \cdot 10^{+39}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10
Accuracy	97.8%
Cost	704

\[x + t \cdot \frac{y - z}{a - z} \]

Alternative 11
Accuracy	70.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 12
Accuracy	59.1%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-193}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	20.5%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023137 
(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))))