
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
def code(x, y, z, t): return x + ((y - x) * (z / t))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
def code(x, y, z, t): return x + ((y - x) * (z / t))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (- y x) (/ t z))))
double code(double x, double y, double z, double t) {
return x + ((y - x) / (t / z));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) / (t / z))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) / (t / z));
}
def code(x, y, z, t): return x + ((y - x) / (t / z))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) / Float64(t / z))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) / (t / z)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y - x}{\frac{t}{z}}
\end{array}
Initial program 98.7%
clear-num98.7%
un-div-inv98.8%
Applied egg-rr98.8%
Final simplification98.8%
(FPCore (x y z t) :precision binary64 (if (or (<= y -2.7e+61) (not (<= y 9e+45))) (+ x (/ y (/ t z))) (+ x (* x (/ z (- t))))))
double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -2.7e+61) || !(y <= 9e+45)) {
tmp = x + (y / (t / z));
} else {
tmp = x + (x * (z / -t));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if ((y <= (-2.7d+61)) .or. (.not. (y <= 9d+45))) then
tmp = x + (y / (t / z))
else
tmp = x + (x * (z / -t))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -2.7e+61) || !(y <= 9e+45)) {
tmp = x + (y / (t / z));
} else {
tmp = x + (x * (z / -t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (y <= -2.7e+61) or not (y <= 9e+45): tmp = x + (y / (t / z)) else: tmp = x + (x * (z / -t)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((y <= -2.7e+61) || !(y <= 9e+45)) tmp = Float64(x + Float64(y / Float64(t / z))); else tmp = Float64(x + Float64(x * Float64(z / Float64(-t)))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((y <= -2.7e+61) || ~((y <= 9e+45))) tmp = x + (y / (t / z)); else tmp = x + (x * (z / -t)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.7e+61], N[Not[LessEqual[y, 9e+45]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -2.7 \cdot 10^{+61} \lor \neg \left(y \leq 9 \cdot 10^{+45}\right):\\
\;\;\;\;x + \frac{y}{\frac{t}{z}}\\
\mathbf{else}:\\
\;\;\;\;x + x \cdot \frac{z}{-t}\\
\end{array}
\end{array}
if y < -2.7000000000000002e61 or 8.9999999999999997e45 < y Initial program 98.9%
clear-num98.9%
un-div-inv99.0%
Applied egg-rr99.0%
Taylor expanded in y around inf 85.4%
associate-/l*93.3%
Simplified93.3%
if -2.7000000000000002e61 < y < 8.9999999999999997e45Initial program 98.6%
clear-num98.6%
un-div-inv98.6%
Applied egg-rr98.6%
Taylor expanded in y around 0 82.6%
associate-*r/82.6%
remove-double-neg82.6%
neg-mul-182.6%
*-commutative82.6%
*-commutative82.6%
times-frac82.6%
metadata-eval82.6%
associate-/r*82.6%
neg-mul-182.6%
remove-double-neg82.6%
times-frac82.6%
neg-mul-182.6%
associate-*r/82.6%
*-commutative82.6%
associate-*l*85.7%
*-commutative85.7%
associate-*l/85.8%
*-lft-identity85.8%
Simplified85.8%
Final simplification88.9%
(FPCore (x y z t) :precision binary64 (if (or (<= y -6.6e+59) (not (<= y 9.2e+45))) (+ x (/ y (/ t z))) (- x (/ x (/ t z)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -6.6e+59) || !(y <= 9.2e+45)) {
tmp = x + (y / (t / z));
} else {
tmp = x - (x / (t / z));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if ((y <= (-6.6d+59)) .or. (.not. (y <= 9.2d+45))) then
tmp = x + (y / (t / z))
else
tmp = x - (x / (t / z))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -6.6e+59) || !(y <= 9.2e+45)) {
tmp = x + (y / (t / z));
} else {
tmp = x - (x / (t / z));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (y <= -6.6e+59) or not (y <= 9.2e+45): tmp = x + (y / (t / z)) else: tmp = x - (x / (t / z)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((y <= -6.6e+59) || !(y <= 9.2e+45)) tmp = Float64(x + Float64(y / Float64(t / z))); else tmp = Float64(x - Float64(x / Float64(t / z))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((y <= -6.6e+59) || ~((y <= 9.2e+45))) tmp = x + (y / (t / z)); else tmp = x - (x / (t / z)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.6e+59], N[Not[LessEqual[y, 9.2e+45]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -6.6 \cdot 10^{+59} \lor \neg \left(y \leq 9.2 \cdot 10^{+45}\right):\\
\;\;\;\;x + \frac{y}{\frac{t}{z}}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{x}{\frac{t}{z}}\\
\end{array}
\end{array}
if y < -6.5999999999999999e59 or 9.20000000000000049e45 < y Initial program 98.9%
clear-num98.9%
un-div-inv99.0%
Applied egg-rr99.0%
Taylor expanded in y around inf 85.4%
associate-/l*93.3%
Simplified93.3%
if -6.5999999999999999e59 < y < 9.20000000000000049e45Initial program 98.6%
Taylor expanded in y around 0 82.6%
mul-1-neg82.6%
associate-/l*85.8%
Simplified85.8%
Final simplification88.9%
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
def code(x, y, z, t): return x + ((y - x) * (z / t))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
Initial program 98.7%
Final simplification98.7%
(FPCore (x y z t) :precision binary64 (+ x (* y (/ z t))))
double code(double x, double y, double z, double t) {
return x + (y * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + (y * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + (y * (z / t));
}
def code(x, y, z, t): return x + (y * (z / t))
function code(x, y, z, t) return Float64(x + Float64(y * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + (y * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + y \cdot \frac{z}{t}
\end{array}
Initial program 98.7%
Taylor expanded in y around inf 70.8%
associate-*r/76.5%
Simplified76.5%
Final simplification76.5%
(FPCore (x y z t) :precision binary64 (+ x (/ y (/ t z))))
double code(double x, double y, double z, double t) {
return x + (y / (t / z));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + (y / (t / z))
end function
public static double code(double x, double y, double z, double t) {
return x + (y / (t / z));
}
def code(x, y, z, t): return x + (y / (t / z))
function code(x, y, z, t) return Float64(x + Float64(y / Float64(t / z))) end
function tmp = code(x, y, z, t) tmp = x + (y / (t / z)); end
code[x_, y_, z_, t_] := N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y}{\frac{t}{z}}
\end{array}
Initial program 98.7%
clear-num98.7%
un-div-inv98.8%
Applied egg-rr98.8%
Taylor expanded in y around inf 70.8%
associate-/l*76.5%
Simplified76.5%
Final simplification76.5%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
(if (< t_1 -1013646692435.8867)
t_2
(if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))
double code(double x, double y, double z, double t) {
double t_1 = (y - x) * (z / t);
double t_2 = x + ((y - x) / (t / z));
double tmp;
if (t_1 < -1013646692435.8867) {
tmp = t_2;
} else if (t_1 < 0.0) {
tmp = x + (((y - x) * z) / t);
} else {
tmp = t_2;
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: t_1
real(8) :: t_2
real(8) :: tmp
t_1 = (y - x) * (z / t)
t_2 = x + ((y - x) / (t / z))
if (t_1 < (-1013646692435.8867d0)) then
tmp = t_2
else if (t_1 < 0.0d0) then
tmp = x + (((y - x) * z) / t)
else
tmp = t_2
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (y - x) * (z / t);
double t_2 = x + ((y - x) / (t / z));
double tmp;
if (t_1 < -1013646692435.8867) {
tmp = t_2;
} else if (t_1 < 0.0) {
tmp = x + (((y - x) * z) / t);
} else {
tmp = t_2;
}
return tmp;
}
def code(x, y, z, t): t_1 = (y - x) * (z / t) t_2 = x + ((y - x) / (t / z)) tmp = 0 if t_1 < -1013646692435.8867: tmp = t_2 elif t_1 < 0.0: tmp = x + (((y - x) * z) / t) else: tmp = t_2 return tmp
function code(x, y, z, t) t_1 = Float64(Float64(y - x) * Float64(z / t)) t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z))) tmp = 0.0 if (t_1 < -1013646692435.8867) tmp = t_2; elseif (t_1 < 0.0) tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t)); else tmp = t_2; end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (y - x) * (z / t); t_2 = x + ((y - x) / (t / z)); tmp = 0.0; if (t_1 < -1013646692435.8867) tmp = t_2; elseif (t_1 < 0.0) tmp = x + (((y - x) * z) / t); else tmp = t_2; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \left(y - x\right) \cdot \frac{z}{t}\\
t_2 := x + \frac{y - x}{\frac{t}{z}}\\
\mathbf{if}\;t_1 < -1013646692435.8867:\\
\;\;\;\;t_2\\
\mathbf{elif}\;t_1 < 0:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\
\mathbf{else}:\\
\;\;\;\;t_2\\
\end{array}
\end{array}
herbie shell --seed 2024020
(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))))