Average Error: 6.4 → 2.7
Time: 8.2s
Precision: binary64
Cost: 1218
Math TeX FPCore C \[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l}
\mathbf{if}\;z \leq -1.1179816606133411 \cdot 10^{+64}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\
\mathbf{elif}\;z \leq 7.433079287520896 \cdot 10^{+172}:\\
\;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\
\end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t} ↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.1179816606133411 \cdot 10^{+64}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\
\mathbf{elif}\;z \leq 7.433079287520896 \cdot 10^{+172}:\\
\;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\
\end{array} (FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t))) ↓
(FPCore (x y z t)
:precision binary64
(if (<= z -1.1179816606133411e+64)
(+ x (* z (/ (- y x) t)))
(if (<= z 7.433079287520896e+172)
(+ x (/ (* z (- y x)) t))
(+ x (* (- y x) (/ z t)))))) double code(double x, double y, double z, double t) {
return x + (((y - x) * z) / t);
}
↓
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -1.1179816606133411e+64) {
tmp = x + (z * ((y - x) / t));
} else if (z <= 7.433079287520896e+172) {
tmp = x + ((z * (y - x)) / t);
} else {
tmp = x + ((y - x) * (z / t));
}
return tmp;
}
Try it out Enter valid numbers for all inputs
Target Original 6.4 Target 1.8 Herbie 2.7
\[\begin{array}{l}
\mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\
\;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\
\mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\
\;\;\;\;x + \frac{y - x}{t} \cdot z\\
\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\
\end{array}\]
Alternatives Alternative 1 Error 1.0 Cost 59200
\[x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{z}}}\]
Alternative 2 Error 2.0 Cost 1218
\[\begin{array}{l}
\mathbf{if}\;x \leq -1.2721410838003617 \cdot 10^{-210}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\
\mathbf{elif}\;x \leq 1.5448624974210764 \cdot 10^{-41}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\
\end{array}\]
Alternative 3 Error 2.2 Cost 904
\[\begin{array}{l}
\mathbf{if}\;y \leq 1.7884550304038338 \cdot 10^{-272} \lor \neg \left(y \leq 3.436078276673044 \cdot 10^{-50}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\
\end{array}\]
Alternative 4 Error 2.0 Cost 904
\[\begin{array}{l}
\mathbf{if}\;t \leq -3.8100894990775214 \cdot 10^{-245} \lor \neg \left(t \leq 3.9280415182811897 \cdot 10^{-218}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\
\end{array}\]
Alternative 5 Error 7.9 Cost 1090
\[\begin{array}{l}
\mathbf{if}\;y \leq -7.801735086200885 \cdot 10^{-46}:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\mathbf{elif}\;y \leq 8.422277528823603 \cdot 10^{-175}:\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z}}\\
\end{array}\]
Alternative 6 Error 8.0 Cost 776
\[\begin{array}{l}
\mathbf{if}\;y \leq -1.3030022012353711 \cdot 10^{-47} \lor \neg \left(y \leq 6.6451556900716525 \cdot 10^{-174}\right):\\
\;\;\;\;x + \frac{y}{\frac{t}{z}}\\
\mathbf{else}:\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\end{array}\]
Alternative 7 Error 17.3 Cost 1090
\[\begin{array}{l}
\mathbf{if}\;x \leq -1.774159551238286 \cdot 10^{-120}:\\
\;\;\;\;x - \frac{x}{\frac{t}{z}}\\
\mathbf{elif}\;x \leq 8.2997827565203 \cdot 10^{-114}:\\
\;\;\;\;y \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\end{array}\]
Alternative 8 Error 17.4 Cost 776
\[\begin{array}{l}
\mathbf{if}\;x \leq -2.6598175863133953 \cdot 10^{-120} \lor \neg \left(x \leq 9.146839396854014 \cdot 10^{-111}\right):\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{z}{t}\\
\end{array}\]
Alternative 9 Error 25.7 Cost 1101
\[\begin{array}{l}
\mathbf{if}\;x \leq -1.2926537485615926 \cdot 10^{-104}:\\
\;\;\;\;x\\
\mathbf{elif}\;x \leq 1.108090910559699 \cdot 10^{-100} \lor \neg \left(x \leq 2.7724922578735122 \cdot 10^{-68}\right) \land x \leq 2.9387611468666887 \cdot 10^{-30}:\\
\;\;\;\;y \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}\]
Alternative 10 Error 25.7 Cost 1101
\[\begin{array}{l}
\mathbf{if}\;x \leq -3.807593210986246 \cdot 10^{-95}:\\
\;\;\;\;x\\
\mathbf{elif}\;x \leq 5.109114698568901 \cdot 10^{-106} \lor \neg \left(x \leq 2.99765774095701 \cdot 10^{-68}\right) \land x \leq 2.9387611468666887 \cdot 10^{-30}:\\
\;\;\;\;\frac{y}{\frac{t}{z}}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}\]
Alternative 11 Error 31.3 Cost 64
\[x\]
Alternative 12 Error 61.8 Cost 64
\[-1\]
Alternative 13 Error 61.8 Cost 64
\[1\]
Error Derivation Split input into 3 regimes if z < -1.11798166061334114e64 Initial program 19.7
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
Using strategy rm Applied associate-/l*_binary64_14004 4.1
\[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
Using strategy rm Applied associate-/r/_binary64_14005 1.8
\[\leadsto x + \color{blue}{\frac{y - x}{t} \cdot z}\]
Simplified1.8
\[\leadsto \color{blue}{x + z \cdot \frac{y - x}{t}}\]
if -1.11798166061334114e64 < z < 7.43307928752089636e172 Initial program 2.6
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
Simplified2.6
\[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{t}}\]
if 7.43307928752089636e172 < z Initial program 25.0
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
Using strategy rm Applied *-un-lft-identity_binary64_14059 25.0
\[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{1 \cdot t}}\]
Applied times-frac_binary64_14065 5.5
\[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]
Simplified5.5
\[\leadsto x + \color{blue}{\left(y - x\right)} \cdot \frac{z}{t}\]
Simplified5.5
\[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}}\]
Recombined 3 regimes into one program. Final simplification2.7
\[\leadsto \begin{array}{l}
\mathbf{if}\;z \leq -1.1179816606133411 \cdot 10^{+64}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\
\mathbf{elif}\;z \leq 7.433079287520896 \cdot 10^{+172}:\\
\;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\
\end{array}\]
Reproduce herbie shell --seed 2021044
(FPCore (x y z t)
:name "Numeric.Histogram:binBounds from Chart-1.5.3"
:precision binary64
:herbie-target
(if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))
(+ x (/ (* (- y x) z) t)))
