Exception for Kahan p9 Example

\[\left(0 < x \land x < 1\right) \land y < 1\]

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - y) * (x + y)) / ((x * x) + (y * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(N[(x - y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2023096 
(FPCore (x y)
  :name "Kahan p9 Example"
  :precision binary64
  :pre (and (and (< 0.0 x) (< x 1.0)) (< y 1.0))

  :herbie-target
  (if (and (< 0.5 (fabs (/ x y))) (< (fabs (/ x y)) 2.0)) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- 1.0 (/ 2.0 (+ 1.0 (* (/ x y) (/ x y))))))

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

Backtrace

match-define: no matching clause for '((x +.f64 (*.f64 (+.f64 x y) (/.f64 (-.f64 x y) (pow.f64 (hypot.f64 x y) 2))) (*.f64 (/.f64 1 (pow.f64 (hypot.f64 x y) 2)) (fma.f64 (neg.f64 y) y (*.f64 y y)))))		L	C
program-body	/home/nightlies/herbie/remove-change/src/programs.rkt	21	0
(unnamed)	/usr/share/racket/collects/racket/contract/private/arrow-higher-order.rkt	379	33
gen-rewrites!	/home/nightlies/herbie/remove-change/src/patch.rkt	145	0
patch-table-run	/home/nightlies/herbie/remove-change/src/patch.rkt	296	0
(unnamed)	/usr/share/racket/collects/racket/contract/private/arrow-val-first.rkt	486	18
run-iter!	/home/nightlies/herbie/remove-change/src/mainloop.rkt	267	0
mutate!	/home/nightlies/herbie/remove-change/src/mainloop.rkt	377	0
run-improve!	/home/nightlies/herbie/remove-change/src/mainloop.rkt	325	0
run-herbie	/home/nightlies/herbie/remove-change/src/sandbox.rkt	57	0
(unnamed)	/home/nightlies/herbie/remove-change/src/sandbox.rkt	133	6
(unnamed)	/usr/share/racket/pkgs/profile-lib/main.rkt	40	10
profile-thunk	/usr/share/racket/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/usr/share/racket/collects/racket/engine.rkt	42	24