Average Error: 2.0 → 1.4
Time: 8.6s
Precision: binary64
Cost: 836
\[x + \left(y - x\right) \cdot \frac{z}{t} \]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) (- INFINITY))
   (* z (- (/ y t) (/ 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 / t) <= -((double) INFINITY)) {
		tmp = z * ((y / t) - (x / t));
	} else {
		tmp = x + ((y - x) * (z / t));
	}
	return tmp;
}

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
↓
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((y / t) - (x / t));
	} else {
		tmp = x + ((y - x) * (z / t));
	}
	return tmp;
}

def code(x, y, z, t):
	return x + ((y - x) * (z / t))
↓
def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = z * ((y / t) - (x / t))
	else:
		tmp = x + ((y - x) * (z / t))
	return tmp

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end
↓
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(y / t) - Float64(x / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / t)));
	end
	return tmp
end

function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end
↓
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = z * ((y / t) - (x / t));
	else
		tmp = x + ((y - x) * (z / t));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], (-Infinity)], N[(z * N[(N[(y / t), $MachinePrecision] - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq -\infty:\\
\;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target2.2
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 z t) < -inf.0

    1. Initial program 64.0

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

    2. Taylor expanded in z around inf 0.3

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

    if -inf.0 < (/.f64 z t)

    1. Initial program 1.4

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternatives

Alternative 1
Error23.5
Cost1944
\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := -\frac{z}{\frac{t}{x}}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error23.5
Cost1944
\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+14}:\\ \;\;\;\;-\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \end{array} \]
Alternative 3
Error13.3
Cost1488
\[\begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error23.1
Cost1362
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25} \lor \neg \left(\frac{z}{t} \leq 6 \cdot 10^{-104} \lor \neg \left(\frac{z}{t} \leq 10^{-43}\right) \land \frac{z}{t} \leq 5 \cdot 10^{-25}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 5
Error23.0
Cost1360
\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error23.7
Cost1360
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;\frac{z}{t} \leq 6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-43}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
Alternative 7
Error2.8
Cost969
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.0005\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
Alternative 8
Error3.7
Cost968
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000000:\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 0.0005:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
Alternative 9
Error1.9
Cost576
\[x + \frac{y - x}{\frac{t}{z}} \]
Alternative 10
Error32.0
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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