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

Average Error: 11.1 → 0.6

Time: 13.2s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-95} \lor \neg \left(t \leq 2 \cdot 10^{-134}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]

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 -4e-95) (not (<= t 2e-134)))
   (+ 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 <= -4e-95) || !(t <= 2e-134)) {
		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 <= (-4d-95)) .or. (.not. (t <= 2d-134))) 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 <= -4e-95) || !(t <= 2e-134)) {
		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 <= -4e-95) or not (t <= 2e-134):
		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 <= -4e-95) || !(t <= 2e-134))
		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 <= -4e-95) || ~((t <= 2e-134)))
		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, -4e-95], N[Not[LessEqual[t, 2e-134]], $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	11.1
Target	0.6
Herbie	0.6

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

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999996e-95 or 2.00000000000000008e-134 < t

   1. Initial program 16.7

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

   2. Simplified 0.7

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

      [Start] 16.7	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 0.7	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -3.99999999999999996e-95 < t < 2.00000000000000008e-134

   1. Initial program 0.4

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-95} \lor \neg \left(t \leq 2 \cdot 10^{-134}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	21.2
Cost	1504

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -6.2:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 200000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 2
Error	21.4
Cost	1504

\[\begin{array}{l} \mathbf{if}\;z \leq -6.2:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 400000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+20}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 3
Error	15.2
Cost	1237

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+20} \lor \neg \left(z \leq 1.6 \cdot 10^{+43}\right) \land z \leq 4.4 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 4
Error	15.1
Cost	1236

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+20}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+43}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 5
Error	14.6
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-5}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 420000:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 6
Error	15.0
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -2.95 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-201}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-304}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-22}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	16.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-201}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-306}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-22}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8
Error	12.1
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-15} \lor \neg \left(a \leq 7.6 \cdot 10^{-23}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 9
Error	16.2
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-8} \lor \neg \left(a \leq 5.5 \cdot 10^{-22}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 10
Error	16.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-22}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 11
Error	1.4
Cost	704

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

Alternative 12
Error	19.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+123}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	26.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Error	51.2
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023060 
(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))))