Herbie run

Date:Tuesday, April 29th, 2025
Commit:688b8b33 on artem-rules-updates
Seed:2025119
Parameters:256 points for 4 iterations
Flags:
reduce:regimesreduce:binary-searchreduce:branch-expressionssetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:proofs
default
Memory:316 247.6 MB

Time bar (total: 5.6min)

series2.8min (49.3%)

Memory
594.5MiB live, 107 921.1MiB allocated; 28.3s collecting garbage
Counts
5 424 → 25 566
Calls

1410 calls:

TimeVariablePointExpression
524.0ms
h
@-inf
((if (>= (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))) (/ (* (floor w) dX.u) (sqrt (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (* (/ dY.u (sqrt (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (floor w))) (>= (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))) (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (* (* (floor w) (floor w)) dX.u) (* (floor w) (floor w)) (floor w) w dX.u (* (* (floor h) (floor h)) (* dX.v dX.v)) (* (floor h) (floor h)) (floor h) h (* dX.v dX.v) dX.v (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h)))) (* (* (floor w) (floor w)) dY.u) dY.u (* (* dY.v dY.v) (* (floor h) (floor h))) (* dY.v dY.v) dY.v (/ (* (floor w) dX.u) (sqrt (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (* (floor w) dX.u) (sqrt (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h)))))) (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))) (* (/ dY.u (sqrt (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (floor w)) (/ dY.u (sqrt (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (sqrt (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h)))))) (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h))))) (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (* (* (floor h) dX.v) dX.v) (* (floor h) dX.v) (* (* dX.u dX.u) (* (floor w) (floor w))) (* dX.u dX.u) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h)))) (* (* (floor w) dY.u) dY.u) (* (floor w) dY.u) (if (>= (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))) (/ (* (floor w) dX.u) (sqrt (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (/ (* (floor w) dY.u) (sqrt (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h)))))))) (>= (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))) (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))) (/ (* (floor w) dY.u) (sqrt (fmax (+ (* (* (* (floor w) (floor w)) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (* (floor w) (floor w)) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (if (>= (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dX.u)) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dY.u))) (>= (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (* (* dX.v dX.v) (* (floor h) (floor h))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* dY.u dY.u) (* (floor w) (floor w))) (* dY.u dY.u) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dX.u)) (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v)) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (floor h) dY.v) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dY.u)) (if (>= (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))) (/ (* (floor w) dX.u) (sqrt (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))))) (/ (* (floor w) dY.u) (sqrt (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) (>= (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))) (* (* (* (floor h) dY.v) dY.v) (floor h)) (* (* (floor h) dY.v) dY.v) (/ (* (floor w) dX.u) (sqrt (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))))) (sqrt (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))) (/ (* (floor w) dY.u) (sqrt (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (sqrt (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (fmax (+ (* (* dX.u dX.u) (* (floor w) (floor w))) (* (* dX.v dX.v) (* (floor h) (floor h)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* dY.u dY.u) (exp (* (log (floor w)) 2))) (exp (* (log (floor w)) 2)) (* (log (floor w)) 2) (log (floor w)) 2 (if (>= (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (* (/ 1 (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))))) (* (floor w) dX.u)) (* (* (sqrt (exp (* (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) -1))) (floor w)) dY.u)) (>= (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (* (* (sqrt (exp (* (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) -1))) (floor w)) dY.u) (* (sqrt (exp (* (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) -1))) (floor w)) (sqrt (exp (* (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) -1))) (exp (* (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) -1)) (* (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) -1) (log (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))))) (fmax (+ (* (* (* (floor h) dX.v) dX.v) (floor h)) (* (* dX.u dX.u) (* (floor w) (floor w)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h)))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* (* (floor h) dY.v) dY.v) (floor h))) (* (* (* (floor w) dY.u) dY.u) (floor w)) -1)
431.0ms
r
@inf
((+ (/ (/ (* (exp (/ (neg r) s)) 1/4) (* (+ (PI) (PI)) s)) r) (/ (* 3/4 (exp (/ (/ (neg r) 3) s))) (* (* (* 6 (PI)) s) r))) (/ (/ (* (exp (/ (neg r) s)) 1/4) (* (+ (PI) (PI)) s)) r) (/ (* (exp (/ (neg r) s)) 1/4) (* (+ (PI) (PI)) s)) (* (/ (exp (/ (neg r) s)) (* (PI) s)) 1/8) (/ (exp (/ (neg r) s)) (* (PI) s)) (exp (/ (neg r) s)) (/ (neg r) s) (neg r) r s (* (PI) s) (PI) 1/8 (/ (* 3/4 (exp (/ (/ (neg r) 3) s))) (* (* (* 6 (PI)) s) r)) (* 3/4 (exp (/ (/ (neg r) 3) s))) 3/4 (exp (/ (/ (neg r) 3) s)) (/ (/ (neg r) 3) s) (/ (neg r) 3) 3 (* (* (* 6 (PI)) s) r) (* (* 6 (PI)) s) (* 6 (PI)) 6 (+ (/ (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r)) (/ (* 3/4 (exp (/ (neg r) (* 3 s)))) (* (* (* 6 (PI)) s) r))) (/ (- (+ (* (/ r (* (* s s) (PI))) 1/144) (+ (* 1/16 (/ r (* (* s s) (PI)))) (/ 1/4 (* (PI) r)))) (/ 1/6 (* (PI) s))) s) (- (+ (* (/ r (* (* s s) (PI))) 1/144) (+ (* 1/16 (/ r (* (* s s) (PI)))) (/ 1/4 (* (PI) r)))) (/ 1/6 (* (PI) s))) (/ 1/4 (* (PI) r)) 1/4 (* (PI) r) (+ (/ (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r)) (/ (* 3/4 (exp (/ (neg r) (* 3 s)))) (* (* (* 6 (PI)) s) r))) (/ 1/4 (* (* (PI) s) r)) (* (* (PI) s) r) (* (+ (* (* (* (* 0 (* (PI) (PI))) s) r) 1/2) (* (PI) r)) s) (+ (* (* (* (* 0 (* (PI) (PI))) s) r) 1/2) (* (PI) r)) (* (* (* 0 (* (PI) (PI))) s) r) (* (* 0 (* (PI) (PI))) s) (* 0 (* (PI) (PI))) 0 (* (PI) (PI)) 1/2 (+ (/ (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r)) (/ (* 3/4 (exp (/ (neg r) (* 3 s)))) (* (* (* 6 (PI)) s) r))) (/ (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r)) (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r) (* (* 2 (PI)) s) (* 2 (PI)) 2 (/ (* 3/4 (exp (/ (neg r) (* 3 s)))) (* (* (* 6 (PI)) s) r)) (/ 1/8 (* (* r s) (PI))) (* (* r s) (PI)) (* r s) (+ (/ (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r)) (/ (* 3/4 (exp (/ (neg r) (* 3 s)))) (* (* (* 6 (PI)) s) r))) (/ (* 1/4 (exp (/ (neg r) s))) (* (* (* 2 (PI)) s) r)) (* (/ (exp (/ (neg r) s)) (* (* (PI) s) r)) 1/8) (/ (exp (/ (neg r) s)) (* (* (PI) s) r)) (* (* (PI) s) r) (/ (* 3/4 (exp (/ (neg r) (* 3 s)))) (* (* (* 6 (PI)) s) r)) (* 3/4 (exp (/ (neg r) (* 3 s)))) (exp (/ (neg r) (* 3 s))) (/ (neg r) (* 3 s)) (* -1/3 (/ r s)) -1/3 (/ r s))
313.0ms
dY.v
@0
((log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* dY.w dY.w) (* (floor d) (floor d))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* dY.w dY.w) (* (floor d) (floor d))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* dY.w dY.w) (* (floor d) (floor d))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))))) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (* (* dX.u dX.u) (* (floor w) (floor w))) (* dX.u dX.u) dX.u (* (floor w) (floor w)) (floor w) w (+ (* (* dY.w dY.w) (* (floor d) (floor d))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h))))) (* dY.w dY.w) dY.w (* (floor d) (floor d)) (floor d) d (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))) (* dY.u dY.u) dY.u (* (* dY.v dY.v) (* (floor h) (floor h))) (* dY.v dY.v) dY.v (* (floor h) (floor h)) (floor h) h (log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (* (* (floor w) (floor w)) (* dX.u dX.u)) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))) (* (* dY.w dY.w) (* (floor d) (floor d))) (log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* (* dX.v dX.v) (floor h)) (floor h)) (* (* (* dX.w dX.w) (floor d)) (floor d))) (* (* dX.v dX.v) (floor h)) (* dX.v dX.v) dX.v (* (* (* dX.w dX.w) (floor d)) (floor d)) (* (* dX.w dX.w) (floor d)) (* dX.w dX.w) dX.w (log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w)) (* (floor d) dX.w) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))) (exp (* (log (* dY.v (floor h))) 2)) (* (log (* dY.v (floor h))) 2) (log (* dY.v (floor h))) (* dY.v (floor h)) 2 (log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))))) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))) (+ (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))) (* (exp (* (log dY.v) 2)) (* (floor h) (floor h))) (exp (* (log dY.v) 2)) (* (log dY.v) 2) (log dY.v))
184.0ms
cosTheta_i
@0
((/ (* (exp (neg (/ (* sinTheta_i sinTheta_O) v))) (/ (* cosTheta_i cosTheta_O) v)) (* (* (sinh (/ 1 v)) 2) v)) (+ (* cosTheta_O (/ cosTheta_i (* (/ (- (exp (* (/ 1 v) 2)) (exp (* (neg (/ 1 v)) 2))) (* 2 (cosh (/ 1 v)))) (* v v)))) (/ (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* (* (* v v) v) (* (sinh (/ 1 v)) 2)))) cosTheta_O (/ cosTheta_i (* (/ (- (exp (* (/ 1 v) 2)) (exp (* (neg (/ 1 v)) 2))) (* 2 (cosh (/ 1 v)))) (* v v))) cosTheta_i (* (/ (- (exp (* (/ 1 v) 2)) (exp (* (neg (/ 1 v)) 2))) (* 2 (cosh (/ 1 v)))) (* v v)) (/ (- (exp (* (/ 1 v) 2)) (exp (* (neg (/ 1 v)) 2))) (* 2 (cosh (/ 1 v)))) (- (exp (* (/ 1 v) 2)) (exp (* (neg (/ 1 v)) 2))) (exp (* (/ 1 v) 2)) (* (/ 1 v) 2) (/ 1 v) 1 v 2 (exp (* (neg (/ 1 v)) 2)) (* (neg (/ 1 v)) 2) (neg (/ 1 v)) (* 2 (cosh (/ 1 v))) (cosh (/ 1 v)) (* v v) (/ (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* (* (* v v) v) (* (sinh (/ 1 v)) 2))) (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O) (* (* sinTheta_O sinTheta_i) cosTheta_i) (* sinTheta_O sinTheta_i) sinTheta_O sinTheta_i (* (* (* v v) v) (* (sinh (/ 1 v)) 2)) (* (* v v) v) (* (sinh (/ 1 v)) 2) (sinh (/ 1 v)) (/ (* (exp (neg (/ (* sinTheta_i sinTheta_O) v))) (/ (* cosTheta_i cosTheta_O) v)) (* (* (sinh (/ 1 v)) 2) v)) (* 1/2 (* cosTheta_O (/ cosTheta_i v))) 1/2 (* cosTheta_O (/ cosTheta_i v)) (/ cosTheta_i v) (/ (/ (/ (* (exp (/ (* sinTheta_O sinTheta_i) (neg v))) (* cosTheta_O cosTheta_i)) v) (* (sinh (/ 1 v)) 2)) v) (/ (/ (* (exp (/ (* sinTheta_O sinTheta_i) (neg v))) (* cosTheta_O cosTheta_i)) v) (* (sinh (/ 1 v)) 2)) (* cosTheta_O (/ cosTheta_i (* (sinh (/ 1 v)) (+ v v)))) (/ cosTheta_i (* (sinh (/ 1 v)) (+ v v))) (* (sinh (/ 1 v)) (+ v v)) (+ v v) (/ (/ (* (* cosTheta_O cosTheta_i) (exp (* sinTheta_O (/ sinTheta_i (neg v))))) (* (sinh (/ 1 v)) (+ v v))) v) (/ (* (* cosTheta_O cosTheta_i) (exp (* sinTheta_O (/ sinTheta_i (neg v))))) (* (sinh (/ 1 v)) (+ v v))) (* (* cosTheta_O cosTheta_i) (exp (* sinTheta_O (/ sinTheta_i (neg v))))) (* cosTheta_O cosTheta_i) (exp (* sinTheta_O (/ sinTheta_i (neg v)))) (* sinTheta_O (/ sinTheta_i (neg v))) (/ sinTheta_i (neg v)) (neg v) (/ (* (exp (neg (/ (* sinTheta_i sinTheta_O) v))) (/ (* cosTheta_i cosTheta_O) v)) (* (* (sinh (/ 1 v)) 2) v)) (+ (* cosTheta_O (/ cosTheta_i (* (* (sinh (/ 1 v)) 2) (* v v)))) (/ (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* (* (* v v) v) (* (sinh (/ 1 v)) 2)))) (/ (+ (* cosTheta_O (/ (* cosTheta_i v) (* 2 (sinh (/ 1 v))))) (/ (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* 2 (sinh (/ 1 v))))) (* (* v v) v)) (+ (* cosTheta_O (/ (* cosTheta_i v) (* 2 (sinh (/ 1 v))))) (/ (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* 2 (sinh (/ 1 v))))) (/ (* cosTheta_i v) (* 2 (sinh (/ 1 v)))) (* cosTheta_i v) (* 2 (sinh (/ 1 v))) (/ (neg (* (* (* sinTheta_O sinTheta_i) cosTheta_i) cosTheta_O)) (* 2 (sinh (/ 1 v)))))
182.0ms
u0
@inf
((/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (/ 1 (+ (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) 1))) (/ 1 (+ (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) 1)) 1 (+ (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) 1) (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0)) (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax))) (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)) (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2)) (+ (PI) (PI)) (PI) u1 (* (PI) 1/2) 1/2 (/ alphay alphax) alphay alphax 2 (* alphay alphay) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax) (- 1 u0) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (+ (* (/ (* (* alphax alphax) u0) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) -1/2) 1) (/ (* (* alphax alphax) u0) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) (* (* alphax alphax) u0) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))) -1/2 (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0)))) (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))) (+ (* (* alphay alphay) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) 1) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))) (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0)))) (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))) (+ (* (/ (+ 1 u0) (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)))) u0) 1) (/ (+ 1 u0) (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)))) (+ 1 u0))

sample52.0s (15.4%)

Memory
589.3MiB live, 61 090.0MiB allocated; 21.9s collecting garbage
Samples
32.2s241 815×0valid
5.7s28 364×1valid
1.2s11 330×0invalid
653.0ms2 268×2valid
211.0ms1 644×1exit
154.0ms751×1invalid
0.0ms1×3valid
Precisions
Click to see histograms. Total time spent on operations: 30.1s
ival-mult!: 9.1s (30.3% of total)
ival-div!: 2.6s (8.6% of total)
ival-exp: 2.1s (7.1% of total)
ival-log: 2.0s (6.7% of total)
ival-fabs: 1.8s (5.9% of total)
ival-sqrt: 1.7s (5.5% of total)
ival-sub!: 1.2s (4% of total)
ival-add!: 1.0s (3.3% of total)
ival-sin: 958.0ms (3.2% of total)
ival-pow2: 954.0ms (3.2% of total)
adjust: 905.0ms (3% of total)
ival-cos: 859.0ms (2.9% of total)
ival-floor: 660.0ms (2.2% of total)
ival-neg: 658.0ms (2.2% of total)
ival-sinu: 588.0ms (2% of total)
ival-<=: 573.0ms (1.9% of total)
ival-cosu: 460.0ms (1.5% of total)
ival-tan: 341.0ms (1.1% of total)
ival-fmax: 299.0ms (1% of total)
ival-and: 294.0ms (1% of total)
ival-log2: 272.0ms (0.9% of total)
ival-if: 207.0ms (0.7% of total)
ival-log1p: 134.0ms (0.4% of total)
ival-asin: 117.0ms (0.4% of total)
ival-atan: 93.0ms (0.3% of total)
ival-sinh: 80.0ms (0.3% of total)
ival->=: 47.0ms (0.2% of total)
ival->: 46.0ms (0.2% of total)
ival-<: 36.0ms (0.1% of total)
ival-assert: 30.0ms (0.1% of total)
ival-pi: 0.0ms (0% of total)
const: 0.0ms (0% of total)
Bogosity

rewrite33.5s (9.9%)

Memory
59.1MiB live, 33 956.8MiB allocated; 13.2s collecting garbage
Stop Event
288×iter-limit
128×node-limit
Counts
30 990 → 63 457

regimes27.4s (8.1%)

Memory
185.9MiB live, 39 473.5MiB allocated; 6.1s collecting garbage
Counts
12 246 → 491
Calls

151 calls:

1.2s
(*.f32 uy #s(literal 2 binary32))
968.0ms
ux
837.0ms
tau
761.0ms
uy
733.0ms
(*.f32 (*.f32 uy #s(literal 2 binary32)) (PI.f32))
Compiler

Compiled 17 379 to 17 951 computations (-3.3% saved)

eval18.3s (5.4%)

Memory
672.4MiB live, 24 931.7MiB allocated; 7.2s collecting garbage
Compiler

Compiled 3 014 046 to 596 993 computations (80.2% saved)

analyze11.4s (3.4%)

Memory
76.5MiB live, 13 623.9MiB allocated; 4.8s collecting garbage
Algorithm
33×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%11.5%88.5%0%0%0%0
52.8%6.1%5.4%88.5%0%0%0%1
54.4%6.2%5.2%88.5%0%0%0%2
54.5%6.3%5.2%88.5%0%0%0%3
55.4%6.4%5.1%88.5%0%0%0%4
62.6%7.2%4.3%88.5%0%0%0%5
66.9%7.6%3.8%88.5%0%0.1%0%6
76.4%8.4%2.6%88.5%0%0.4%0%7
76.8%8.5%2.6%88.5%0%0.4%0%8
81.4%9%2%88.5%0%0.4%0%9
85.1%9.3%1.6%88.5%0%0.5%0%10
86.3%9.4%1.5%88.5%0%0.5%0%11
87.3%9.5%1.4%88.5%0%0.6%0%12
Compiler

Compiled 2 648 to 1 113 computations (58% saved)

derivations10.9s (3.2%)

Memory
232.2MiB live, 9 821.3MiB allocated; 1.5s collecting garbage
Stop Event
31×fuel
1×done
Compiler

Compiled 8 414 to 3 693 computations (56.1% saved)

prune10.4s (3.1%)

Memory
-288.7MiB live, 15 629.8MiB allocated; 3.7s collecting garbage
Counts
156 068 → 3 854
Compiler

Compiled 320 315 to 204 101 computations (36.3% saved)

preprocess5.9s (1.7%)

Memory
-84.1MiB live, 9 054.9MiB allocated; 1.2s collecting garbage
Stop Event
33×node-limit
Compiler

Compiled 84 356 to 52 211 computations (38.1% saved)

bsearch757.0ms (0.2%)

Memory
-35.8MiB live, 734.6MiB allocated; 159ms collecting garbage
Algorithm
91×binary-search
47×left-value
Stop Event
91×narrow-enough
Samples
279.0ms1 344×1valid
73.0ms947×0valid
66.0ms211×1invalid
46.0ms189×2valid
20.0ms370×0invalid
Compiler

Compiled 13 722 to 12 784 computations (6.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 345.0ms
ival-exp: 150.0ms (43.5% of total)
ival-mult!: 50.0ms (14.5% of total)
adjust: 39.0ms (11.3% of total)
ival-pow2: 29.0ms (8.4% of total)
ival-log1p: 26.0ms (7.5% of total)
ival-sub!: 17.0ms (4.9% of total)
ival-sqrt: 13.0ms (3.8% of total)
ival-fabs: 11.0ms (3.2% of total)
ival-add!: 10.0ms (2.9% of total)

start4.0ms (0%)

Memory
9.5MiB live, 9.4MiB allocated; 0ms collecting garbage

end0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Calls

1 calls:

TimeVariablePointExpression
2.4min
u1
@0
((/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (/ 1 (+ (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) 1))) (/ 1 (+ (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) 1)) 1 (+ (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) 1) (/ u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0))) u0 (* (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (- 1 u0)) (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax))) (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)) (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2)) (+ (PI) (PI)) (PI) u1 (* (PI) 1/2) 1/2 (/ alphay alphax) alphay alphax 2 (* alphay alphay) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax) (- 1 u0) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (+ (* (/ (* (* alphax alphax) u0) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) -1/2) 1) (/ (* (* alphax alphax) u0) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) (* (* alphax alphax) u0) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))) -1/2 (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0)))) (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))) (+ (* (* alphay alphay) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) 1) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))) (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))))) (sqrt (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0)))) (+ 1 (/ (* (/ 1 (+ (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (/ (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphay alphay)))) u0) (- 1 u0))) (+ (* (/ (+ 1 u0) (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)))) u0) 1) (/ (+ 1 u0) (+ (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)))) (+ 1 u0))

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