\[\left(0 < cosTheta \land cosTheta < 0.9999\right) \land \left(-1 < c \land c < 1\right)\]

\[\frac{1}{\left(1 + c\right) + \left(\frac{1}{\sqrt{\pi}} \cdot \frac{\sqrt{\left(1 - cosTheta\right) - cosTheta}}{cosTheta}\right) \cdot e^{\left(-cosTheta\right) \cdot cosTheta}} \]

(FPCore (cosTheta c)
 :precision binary32
 (/
  1.0
  (+
   (+ 1.0 c)
   (*
    (* (/ 1.0 (sqrt PI)) (/ (sqrt (- (- 1.0 cosTheta) cosTheta)) cosTheta))
    (exp (* (- cosTheta) cosTheta))))))

float code(float cosTheta, float c) {
	return 1.0f / ((1.0f + c) + (((1.0f / sqrtf(((float) M_PI))) * (sqrtf(((1.0f - cosTheta) - cosTheta)) / cosTheta)) * expf((-cosTheta * cosTheta))));
}

function code(cosTheta, c)
	return Float32(Float32(1.0) / Float32(Float32(Float32(1.0) + c) + Float32(Float32(Float32(Float32(1.0) / sqrt(Float32(pi))) * Float32(sqrt(Float32(Float32(Float32(1.0) - cosTheta) - cosTheta)) / cosTheta)) * exp(Float32(Float32(-cosTheta) * cosTheta)))))
end

function tmp = code(cosTheta, c)
	tmp = single(1.0) / ((single(1.0) + c) + (((single(1.0) / sqrt(single(pi))) * (sqrt(((single(1.0) - cosTheta) - cosTheta)) / cosTheta)) * exp((-cosTheta * cosTheta))));
end

\frac{1}{\left(1 + c\right) + \left(\frac{1}{\sqrt{\pi}} \cdot \frac{\sqrt{\left(1 - cosTheta\right) - cosTheta}}{cosTheta}\right) \cdot e^{\left(-cosTheta\right) \cdot cosTheta}}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2022203 
(FPCore (cosTheta c)
  :name "Beckmann Sample, normalization factor"
  :precision binary32
  :pre (and (and (< 0.0 cosTheta) (< cosTheta 0.9999)) (and (< -1.0 c) (< c 1.0)))
  (/ 1.0 (+ (+ 1.0 c) (* (* (/ 1.0 (sqrt PI)) (/ (sqrt (- (- 1.0 cosTheta) cosTheta)) cosTheta)) (exp (* (- cosTheta) cosTheta))))))

Backtrace

hash-ref: no value found for key key: '~		L	C
get-parametric-operator	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/syntax.rkt	218	0
f336	.../match/compiler.rkt	548	40
expand-parametric	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/sugar.rkt	62	0
(unnamed)	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	176	8
generate-rules-for	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	161	0
generate-missing-rules	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	187	0
(unnamed)	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	29	26
get-swaps	/data/pavpan/nightlies/herbie/enumo-rat/src/symmetry.rkt	6	0
connected-components	/data/pavpan/nightlies/herbie/enumo-rat/src/symmetry.rkt	17	0
run-improve!	/data/pavpan/nightlies/herbie/enumo-rat/src/mainloop.rkt	296	0
(unnamed)	/data/pavpan/nightlies/herbie/enumo-rat/src/sandbox.rkt	55	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