(FPCore (x y z t a) :precision binary64 (- (+ x y) (/ (* (- z t) y) (- a t))))
(FPCore (x y z t a)
:precision binary64
(let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
(if (<= t_1 (- INFINITY))
(+ (* (/ y (/ t (- z a))) (/ a t)) (- x (/ y (/ t (- a z)))))
(if (<= t_1 -2e-148)
t_1
(if (<= t_1 0.0)
(+ x (* y (/ (- z a) t)))
(+ x (fma y (/ (- z t) (- t a)) y)))))))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 t_1 = (x + y) + ((y * (t - z)) / (a - t));
double tmp;
if (t_1 <= -((double) INFINITY)) {
tmp = ((y / (t / (z - a))) * (a / t)) + (x - (y / (t / (a - z))));
} else if (t_1 <= -2e-148) {
tmp = t_1;
} else if (t_1 <= 0.0) {
tmp = x + (y * ((z - a) / t));
} else {
tmp = x + fma(y, ((z - t) / (t - a)), y);
}
return tmp;
}
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) t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t))) tmp = 0.0 if (t_1 <= Float64(-Inf)) tmp = Float64(Float64(Float64(y / Float64(t / Float64(z - a))) * Float64(a / t)) + Float64(x - Float64(y / Float64(t / Float64(a - z))))); elseif (t_1 <= -2e-148) tmp = t_1; elseif (t_1 <= 0.0) tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t))); else tmp = Float64(x + fma(y, Float64(Float64(z - t) / Float64(t - a)), y)); end return tmp end
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_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision] + N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-148], t$95$1, If[LessEqual[t$95$1, 0.0], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]]]]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
\begin{array}{l}
t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\
\mathbf{if}\;t_1 \leq -\infty:\\
\;\;\;\;\frac{y}{\frac{t}{z - a}} \cdot \frac{a}{t} + \left(x - \frac{y}{\frac{t}{a - z}}\right)\\
\mathbf{elif}\;t_1 \leq -2 \cdot 10^{-148}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;t_1 \leq 0:\\
\;\;\;\;x + y \cdot \frac{z - a}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \mathsf{fma}\left(y, \frac{z - t}{t - a}, y\right)\\
\end{array}
| Original | 16.2 |
|---|---|
| Target | 8.6 |
| Herbie | 5.5 |
if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0Initial program 64.0
Simplified28.6
Taylor expanded in t around -inf 43.6
Simplified20.8
if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999987e-148Initial program 1.4
if -1.99999999999999987e-148 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0Initial program 47.2
Simplified27.9
Taylor expanded in t around inf 55.8
Simplified13.1
Taylor expanded in y around 0 9.2
Simplified9.2
if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) Initial program 12.2
Simplified5.1
Final simplification5.5
| Alternative 1 | |
|---|---|
| Error | 8.8 |
| Cost | 4432 |
| Alternative 2 | |
|---|---|
| Error | 8.8 |
| Cost | 4432 |
| Alternative 3 | |
|---|---|
| Error | 7.3 |
| Cost | 1096 |
| Alternative 4 | |
|---|---|
| Error | 22.8 |
| Cost | 844 |
| Alternative 5 | |
|---|---|
| Error | 13.1 |
| Cost | 840 |
| Alternative 6 | |
|---|---|
| Error | 10.4 |
| Cost | 840 |
| Alternative 7 | |
|---|---|
| Error | 14.0 |
| Cost | 712 |
| Alternative 8 | |
|---|---|
| Error | 21.5 |
| Cost | 588 |
| Alternative 9 | |
|---|---|
| Error | 21.5 |
| Cost | 588 |
| Alternative 10 | |
|---|---|
| Error | 19.8 |
| Cost | 456 |
| Alternative 11 | |
|---|---|
| Error | 28.7 |
| Cost | 64 |
herbie shell --seed 2022329
(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))))