Herbie run

Date:Wednesday, April 30th, 2025
Commit:77680327 on prove-soundness
Seed:2025120
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:567 508.3 MB

Time bar (total: 8.9min)

sample3.5min (39.6%)

Memory
2 625.5MiB live, 172 200.2MiB allocated; 1.3min collecting garbage
Samples
2.0min18 799×3exit
42.8s269 053×0valid
4.8s28 600×1valid
1.1s11 095×0invalid
675.0ms2 429×2valid
178.0ms1 602×1exit
146.0ms689×1invalid
60.0ms5×5exit
58.0ms5×4exit
0.0ms1×4valid
Precisions
Click to see histograms. Total time spent on operations: 2.6min
ival-mult!: 25.0s (16.1% of total)
ival-pow2: 20.4s (13.2% of total)
ival-log: 19.5s (12.6% of total)
adjust: 19.0s (12.3% of total)
ival-exp: 18.3s (11.8% of total)
ival-div!: 10.3s (6.6% of total)
ival-sub!: 8.0s (5.2% of total)
ival-add!: 7.2s (4.6% of total)
ival-sqrt: 5.6s (3.6% of total)
ival-neg: 5.6s (3.6% of total)
ival-fmax: 4.2s (2.7% of total)
ival-fmin: 3.1s (2% of total)
ival-sin: 1.4s (0.9% of total)
ival-fabs: 1.4s (0.9% of total)
ival-cos: 1.3s (0.8% of total)
ival-floor: 828.0ms (0.5% of total)
ival-sinu: 629.0ms (0.4% of total)
ival-<=: 594.0ms (0.4% of total)
ival-expm1: 470.0ms (0.3% of total)
ival-and: 457.0ms (0.3% of total)
ival-cosu: 407.0ms (0.3% of total)
ival-tan: 271.0ms (0.2% of total)
ival-if: 228.0ms (0.1% of total)
ival-log2: 199.0ms (0.1% of total)
ival-log1p: 136.0ms (0.1% of total)
ival-sinh: 135.0ms (0.1% of total)
ival-atan: 117.0ms (0.1% of total)
ival->=: 105.0ms (0.1% of total)
ival-asin: 103.0ms (0.1% of total)
ival->: 53.0ms (0% of total)
ival-assert: 30.0ms (0% of total)
ival-<: 24.0ms (0% of total)
const: 3.0ms (0% of total)
ival-pi: 0.0ms (0% of total)
Bogosity

series2.8min (31.9%)

Memory
3 539.3MiB live, 219 549.8MiB allocated; 1.3min collecting garbage
Counts
6 099 → 27 846
Calls

1497 calls:

TimeVariablePointExpression
470.0ms
y
@inf
((fmax (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (/ (+ (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (+ (* z 30) (* 30 x)))) 2))) 1/5)) (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2)) (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* x 30) 2) (* x 30) x 30 2 (pow (* y 30) 2) (* y 30) y (pow (* z 30) 2) (* z 30) z 25 (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (/ (+ (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (+ (* z 30) (* 30 x)))) 2))) 1/5) (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (/ (+ (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (+ (* z 30) (* 30 x)))) 2))) (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (/ (+ (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (+ (* z 30) (* 30 x)))) 2)) (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* x 30)) (cos (* y 30))) (sin (* x 30)) (cos (* y 30)) (* (sin (* y 30)) (cos (* z 30))) (sin (* y 30)) (cos (* z 30)) (/ (+ (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (+ (* z 30) (* 30 x)))) 2) (+ (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (+ (* z 30) (* 30 x)))) (+ (* (sin (* -30 x)) (cos (* z 30))) (* (cos (* -30 x)) (sin (* z 30)))) (sin (* -30 x)) (* -30 x) -30 (* (cos (* -30 x)) (sin (* z 30))) (cos (* -30 x)) (sin (* z 30)) (sin (+ (* z 30) (* 30 x))) (+ (* z 30) (* 30 x)) (* 30 x) 1/5 (fmax (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5)) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5) (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30)))) (+ (* (sin (* 30 x)) (cos (* y 30))) (sin (* y 30))) (sin (* 30 x)) (fmax (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5)) (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5) (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30)))) (+ (* (sin (* 30 x)) (cos (* y 30))) (sin (* y 30))) (fmax (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5)) (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2)) (* (* y y) 900) (* y y) 900 (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5) (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30)))) (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))) (cos (* x 30)) (fmax (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (- (fabs (+ (+ (* (sin (* x 30)) (cos (* y 30))) (* (sin (* y 30)) (cos (* z 30)))) (* (sin (* z 30)) (cos (* x 30))))) 1/5)) (- (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) 25) (sqrt (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2))) (+ (+ (pow (* x 30) 2) (pow (* y 30) 2)) (pow (* z 30) 2)) (+ (pow (* x 30) 2) (pow (* y 30) 2)) (* (+ (* (/ (* y y) (* x x)) 900) 900) (* x x)) (+ (* (/ (* y y) (* x x)) 900) 900) (/ (* y y) (* x x)) (* x x))
442.0ms
h
@inf
((if (>= (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))) (/ (* (floor h) dX.v) (sqrt (fmax (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (/ (* (floor h) dY.v) (sqrt (fmax (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h)))))))) (>= (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) -1 (* (/ 1 (floor w)) (/ -1 (floor w))) (/ 1 (floor w)) 1 (floor w) w (/ -1 (floor w)) dX.u (* (* (floor h) (floor h)) (* dX.v dX.v)) (* (floor h) (floor h)) (floor h) h (* dX.v dX.v) dX.v (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h)))) (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u (* (* dY.v dY.v) (* (floor h) (floor h))) (* dY.v dY.v) dY.v (/ (* (floor h) dX.v) (sqrt (fmax (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (* (floor h) dX.v) (sqrt (fmax (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h)))))) (fmax (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))) (/ (* (floor h) dY.v) (sqrt (fmax (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* (/ -1 (* (/ 1 (floor w)) (/ -1 (floor w)))) dY.u) dY.u) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (* (floor h) dY.v) (if (>= (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (* (floor w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h))))) (* dX.v (/ (floor h) (sqrt (fmax (+ (* (* (* (/ 1 (pow (floor w) -1)) (/ 1 (pow (floor w) -1))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))))))) (/ (* (floor h) dY.v) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (* (floor w) dY.u) dY.u) (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 w) dY.u) dY.u) (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))) (* (* dX.v dX.v) (* (floor h) (floor h))) (+ (* (* (* (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) (* dX.v (/ (floor h) (sqrt (fmax (+ (* (* (* (/ 1 (pow (floor w) -1)) (/ 1 (pow (floor w) -1))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))))))) (/ (floor h) (sqrt (fmax (+ (* (* (* (/ 1 (pow (floor w) -1)) (/ 1 (pow (floor w) -1))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h))))))) (sqrt (fmax (+ (* (* (* (/ 1 (pow (floor w) -1)) (/ 1 (pow (floor w) -1))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))))) (fmax (+ (* (* (* (/ 1 (pow (floor w) -1)) (/ 1 (pow (floor w) -1))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h))))) (+ (* (* (* (/ 1 (pow (floor w) -1)) (/ 1 (pow (floor w) -1))) dX.u) dX.u) (* (* (floor h) (floor h)) (* dX.v dX.v))) (+ (* (* dY.u dY.u) (* (floor w) (floor w))) (* (* dY.v dY.v) (* (floor h) (floor h)))) (* dY.u dY.u) (* (floor w) (floor w)) (/ (* (floor h) dY.v) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (* (floor w) dY.u) dY.u) (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 w) dY.u) dY.u) (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 w) dY.u) dY.u) (floor w)) (* (* dY.v dY.v) (* (floor h) (floor h))))) (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 h) dX.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 h) dY.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) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor w) (floor w)) (* dX.u dX.u)) (* dX.u dX.u) (+ (* (* (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)) (* (/ 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 h) dX.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)))))) (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)))) (* (/ 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 h) dY.v)) (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 h) dX.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 h) dY.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) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (exp (* (log (* (floor h) dX.v)) 2)) (* (log (* (floor h) dX.v)) 2) (log (* (floor h) dX.v)) 2 (* (/ 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 h) dX.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)))))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* 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243.0ms
u0
@inf
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220.0ms
u0
@-inf
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(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) (/ 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))))) (+ (* (* -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) (* alphay alphay)) 1) (* -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0))) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) 4 (* (- 1 u0) (- 1 u0)) -3/4 (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax)))) (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))) (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax)) (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)))
213.0ms
u0
@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))))) (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) (/ 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))))) (+ (* (* -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) (* alphay alphay)) 1) (* -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0))) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) 4 (* (- 1 u0) (- 1 u0)) -3/4 (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax)))) (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))) (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax)) (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)))

rewrite34.4s (6.5%)

Memory
775.4MiB live, 36 604.8MiB allocated; 12.7s collecting garbage
Stop Event
320×iter-limit
140×node-limit
Counts
33 945 → 67 513

regimes33.9s (6.4%)

Memory
2 144.6MiB live, 44 767.2MiB allocated; 15.8s collecting garbage
Counts
12 498 → 621
Calls

158 calls:

2.4s
cosTheta
2.2s
n1_i
1.3s
(*.f32 uy #s(literal 2 binary32))
886.0ms
(log.f32 (-.f32 #s(literal 1 binary32) u0))
866.0ms
ux
Compiler

Compiled 20 199 to 19 591 computations (3% saved)

analyze33.7s (6.3%)

Memory
584.6MiB live, 36 333.9MiB allocated; 19.8s collecting garbage
Algorithm
37×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%21%79%0%0%0%0
25.7%5.4%15.6%79%0%0%0%1
26.5%5.6%15.5%79%0%0%0%2
26.5%5.6%15.4%79%0%0%0%3
28.6%6%15%79%0%0%0%4
40.9%8.6%12.4%79%0%0%0%5
46.2%9.7%11.3%79%0%0%0%6
53.2%11%9.7%79%0%0.4%0%7
55.6%11.5%9.2%79%0%0.4%0%8
60.6%12.5%8.1%79%0%0.4%0%9
63.8%13.1%7.4%79%0%0.5%0%10
66.1%13.6%7%79%0%0.5%0%11
67.5%13.9%6.7%79%0%0.5%0%12
Compiler

Compiled 20 293 to 1 873 computations (90.8% saved)

derivations19.3s (3.6%)

Memory
-205.4MiB live, 15 779.7MiB allocated; 6.0s collecting garbage
Stop Event
34×fuel
1×done
Compiler

Compiled 13 377 to 4 597 computations (65.6% saved)

eval13.4s (2.5%)

Memory
-277.1MiB live, 17 005.5MiB allocated; 7.5s collecting garbage
Compiler

Compiled 2 485 691 to 448 238 computations (82% saved)

prune8.3s (1.6%)

Memory
-393.0MiB live, 12 541.4MiB allocated; 2.7s collecting garbage
Counts
69 798 → 4 154
Compiler

Compiled 365 518 to 219 299 computations (40% saved)

preprocess7.4s (1.4%)

Memory
-276.9MiB live, 10 854.8MiB allocated; 1.7s collecting garbage
Stop Event
36×node-limit
Compiler

Compiled 101 260 to 57 187 computations (43.5% saved)

bsearch1.2s (0.2%)

Memory
52.7MiB live, 1 815.6MiB allocated; 215ms collecting garbage
Algorithm
134×binary-search
90×left-value
Stop Event
131×narrow-enough
3×predicate-same
Samples
368.0ms2 512×0valid
265.0ms1 328×1valid
44.0ms216×1invalid
29.0ms521×0invalid
25.0ms96×2valid
Compiler

Compiled 27 787 to 20 656 computations (25.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 583.0ms
ival-exp: 157.0ms (26.9% of total)
ival-sin: 69.0ms (11.8% of total)
ival-pow2: 62.0ms (10.6% of total)
ival-mult!: 58.0ms (9.9% of total)
ival-sub!: 43.0ms (7.4% of total)
ival-fmax: 39.0ms (6.7% of total)
adjust: 36.0ms (6.2% of total)
ival-log1p: 29.0ms (5% of total)
ival-cos: 27.0ms (4.6% of total)
ival-add!: 22.0ms (3.8% of total)
ival-sqrt: 18.0ms (3.1% of total)
ival-fabs: 11.0ms (1.9% of total)
ival-fmin: 10.0ms (1.7% of total)
ival-neg: 5.0ms (0.9% of total)

start84.0ms (0%)

Memory
-16.2MiB live, 54.9MiB allocated; 125ms collecting garbage

end0.0ms (0%)

Memory
0.8MiB 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))))) (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) (/ 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))))) (+ (* (* -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) (* alphay alphay)) 1) (* -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) -1/2 (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (* alphay alphay)) (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) -3/4) (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))))) (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0))) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) 4 (* (- 1 u0) (- 1 u0)) -3/4 (neg (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax)))) (/ (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax))) (* (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) u0) (* (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)) (* alphax alphax)) (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4)))

Profiling

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