Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Error: 24.4 → 4.7

Time: 6.5s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (+ (/ y (/ (- a t) (- z t))) (* x (- (+ (/ t (- a t)) 1.0) (/ z (- a t))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	return (y / ((a - t) / (z - t))) + (x * (((t / (a - t)) + 1.0) - (z / (a - t))));
}

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 - x) * (z - t)) / (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
    code = (y / ((a - t) / (z - t))) + (x * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	return (y / ((a - t) / (z - t))) + (x * (((t / (a - t)) + 1.0) - (z / (a - t))));
}

Python

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

↓

def code(x, y, z, t, a):
	return (y / ((a - t) / (z - t))) + (x * (((t / (a - t)) + 1.0) - (z / (a - t))))

Julia

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

↓

function code(x, y, z, t, a)
	return Float64(Float64(y / Float64(Float64(a - t) / Float64(z - t))) + Float64(x * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t)))))
end

MATLAB

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

↓

function tmp = code(x, y, z, t, a)
	tmp = (y / ((a - t) / (z - t))) + (x * (((t / (a - t)) + 1.0) - (z / (a - t))));
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := N[(N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	24.4
Target	9.7
Herbie	4.7

\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Initial program 24.4

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

2. Simplified 15.0

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

3. Taylor expanded in x around -inf 15.1

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

4. Simplified 7.8

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

5. Applied egg-rr 7.9

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

6. Applied egg-rr 4.7

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

7. Final simplification 4.7

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

Reproduce

herbie shell --seed 2022192 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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