Herbie run

Date:Thursday, May 22nd, 2025
Commit:089dffb0 on main
Seed:2025142
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:629 134.1 MB

Time bar (total: 8.6min)

sample3.6min (42.1%)

Memory
5 098.1MiB live, 259 806.7MiB allocated; 1.8min collecting garbage
Samples
2.1min15 150×3exit
41.8s268 314×0valid
5.0s28 732×1valid
1.1s11 281×0invalid
629.0ms2 486×2valid
196.0ms1 652×1exit
125.0ms680×1invalid
66.0ms5×5exit
59.0ms4×4exit
1.0ms2×4valid
0.0ms1×3valid
Precisions
Click to see histograms. Total time spent on operations: 2.5min
ival-pow2: 22.1s (14.5% of total)
ival-mult!: 22.1s (14.5% of total)
ival-exp: 20.4s (13.4% of total)
adjust: 20.3s (13.3% of total)
ival-log: 17.8s (11.7% of total)
ival-div!: 10.3s (6.7% of total)
ival-add!: 7.3s (4.8% of total)
ival-neg: 7.3s (4.8% of total)
ival-sub!: 7.2s (4.7% of total)
ival-sqrt: 5.9s (3.9% of total)
ival-fmax: 2.2s (1.4% of total)
ival-fabs: 1.7s (1.1% of total)
ival-sin: 1.5s (1% of total)
ival-fmin: 1.0s (0.7% of total)
ival-cos: 886.0ms (0.6% of total)
ival-floor: 833.0ms (0.5% of total)
ival-sinu: 632.0ms (0.4% of total)
ival-<=: 544.0ms (0.4% of total)
ival-expm1: 454.0ms (0.3% of total)
ival-cosu: 406.0ms (0.3% of total)
ival-if: 315.0ms (0.2% of total)
ival-and: 308.0ms (0.2% of total)
ival-tan: 293.0ms (0.2% of total)
ival-log2: 193.0ms (0.1% of total)
ival-log1p: 169.0ms (0.1% of total)
ival-asin: 134.0ms (0.1% of total)
ival->: 105.0ms (0.1% of total)
ival-atan: 92.0ms (0.1% of total)
ival-sinh: 89.0ms (0.1% of total)
ival->=: 43.0ms (0% of total)
ival-<: 31.0ms (0% of total)
ival-assert: 30.0ms (0% of total)
const: 1.0ms (0% of total)
ival-pi: 0.0ms (0% of total)
Bogosity

series2.8min (32.8%)

Memory
2 327.4MiB live, 204 283.6MiB allocated; 1.3min collecting garbage
Counts
6 240 → 20 664
Calls

1488 calls:

TimeVariablePointExpression
638.0ms
u1
@-inf
((* (sqrt (/ u1 (/ (- 1 (* u1 u1)) (+ 1 u1)))) (sin (* 314159265359/50000000000 u2))) (sqrt (/ u1 (/ (- 1 (* u1 u1)) (+ 1 u1)))) (/ u1 (/ (- 1 (* u1 u1)) (+ 1 u1))) u1 (/ (- 1 (* u1 u1)) (+ 1 u1)) (- 1 (* u1 u1)) 1 (* u1 u1) (+ 1 u1) (* (+ (/ 1 u1) 1) u1) (+ (/ 1 u1) 1) (/ 1 u1) (sin (* 314159265359/50000000000 u2)) (* 314159265359/50000000000 u2) 314159265359/50000000000 u2 (* (sqrt (/ u1 (- 1 u1))) (sin (* 314159265359/50000000000 u2))) (* (* (sqrt (/ u1 (- 1 u1))) u2) 314159265359/50000000000) (* (sqrt (/ u1 (- 1 u1))) u2) (* (sqrt u1) u2) (sqrt u1) (* (sqrt (/ u1 (- 1 u1))) (sin (* 314159265359/50000000000 u2))) (sqrt (/ u1 (- 1 u1))) (/ u1 (- 1 u1)) (- 1 u1) (sin (* 314159265359/50000000000 u2)) (* (+ (* (* u2 u2) -31006276680305942139213528068663279/750000000000000000000000000000000) 314159265359/50000000000) u2) (+ (* (* u2 u2) -31006276680305942139213528068663279/750000000000000000000000000000000) 314159265359/50000000000) (* u2 u2) -31006276680305942139213528068663279/750000000000000000000000000000000 (* (sqrt (/ u1 (- 1 u1))) (sin (* 314159265359/50000000000 u2))) (* (+ (* (* (* u2 u2) -31006276680305942139213528068663279/750000000000000000000000000000000) (sqrt (/ u1 (- 1 u1)))) (/ (* (sqrt u1) 314159265359/50000000000) (sqrt (- 1 u1)))) u2) (+ (* (* (* u2 u2) -31006276680305942139213528068663279/750000000000000000000000000000000) (sqrt (/ u1 (- 1 u1)))) (/ (* (sqrt u1) 314159265359/50000000000) (sqrt (- 1 u1)))) (* (* u2 u2) -31006276680305942139213528068663279/750000000000000000000000000000000) (/ (* (sqrt u1) 314159265359/50000000000) (sqrt (- 1 u1))) (* (sqrt u1) 314159265359/50000000000) (sqrt (- 1 u1)) (/ (* (sqrt u1) (sin (* u2 314159265359/50000000000))) (sqrt (- 1 u1))) (* (sqrt u1) (sin (* u2 314159265359/50000000000))) (sin (* u2 314159265359/50000000000)) (* u2 314159265359/50000000000))
446.0ms
s
@-inf
((* (* 3 s) (log (/ 1 (- 1 (/ (- u 1/4) 3/4))))) (* 3 s) 3 s (log (/ 1 (- 1 (/ (- u 1/4) 3/4)))) (/ 1 (- 1 (/ (- u 1/4) 3/4))) 1 (- 1 (/ (- u 1/4) 3/4)) (/ (- u 1/4) 3/4) (- u 1/4) u 1/4 3/4)
402.0ms
dY.w
@inf
((log2 (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (exp (* (log (floor d)) 1)) dX.w) (* (exp (* (log (floor d)) 1)) dX.w))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (exp (* (log (floor d)) 1)) dY.w) (* (exp (* (log (floor d)) 1)) dY.w)))))) (sqrt (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (exp (* (log (floor d)) 1)) dX.w) (* (exp (* (log (floor d)) 1)) dX.w))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (exp (* (log (floor d)) 1)) dY.w) (* (exp (* (log (floor d)) 1)) dY.w))))) (fmax (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (exp (* (log (floor d)) 1)) dX.w) (* (exp (* (log (floor d)) 1)) dX.w))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (exp (* (log (floor d)) 1)) dY.w) (* (exp (* (log (floor d)) 1)) dY.w)))) (+ (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (exp (* (log (floor d)) 1)) dX.w) (* (exp (* (log (floor d)) 1)) dX.w))) (+ (* (* (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 w) dX.u) (floor w) w dX.u (* (* (floor h) dX.v) (* (floor h) dX.v)) (* (floor h) dX.v) (floor h) h dX.v (* (* (exp (* (log (floor d)) 1)) dX.w) (* (exp (* (log (floor d)) 1)) dX.w)) (* (exp (* (log (floor d)) 1)) dX.w) (exp (* (log (floor d)) 1)) (* (log (floor d)) 1) (log (floor d)) (floor d) d 1 dX.w (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (exp (* (log (floor d)) 1)) dY.w) (* (exp (* (log (floor d)) 1)) dY.w))) (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (exp (* (log (* (floor w) dY.u)) 2)) (* (log (* (floor w) dY.u)) 2) (log (* (floor w) dY.u)) (* (floor w) dY.u) dY.u 2 (* (* (floor h) dY.v) (* (floor h) dY.v)) (* (floor h) dY.v) dY.v (* (* (exp (* (log (floor d)) 1)) dY.w) (* (exp (* (log (floor d)) 1)) dY.w)) (* (exp (* (log (floor d)) 1)) dY.w) dY.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))) (+ (* (* dX.w dX.w) (* (floor d) (floor d))) (* (* (floor w) (floor w)) (* dX.u dX.u))) (* dX.w dX.w) (* (floor d) (floor d)) (* (* (floor w) (floor w)) (* dX.u dX.u)) (* (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))) (* (* dY.u dY.u) (* (floor w) (floor w)))) (* dY.w dY.w) (* (* dY.u dY.u) (* (floor w) (floor w))) (* dY.u dY.u) (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))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (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))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (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))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w)))) (+ (+ (exp (* (log (* (floor w) dY.u)) 2)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor d) dY.w) (* (floor d) dY.w))) (* (* (floor d) dY.w) (* (floor d) dY.w)) (* (floor d) dY.w) (log2 (exp (* (log (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 h) dY.v) (floor h)) dY.v) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d))))))) 1/2))) (exp (* (log (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 h) dY.v) (floor h)) dY.v) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d))))))) 1/2)) (* (log (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 h) dY.v) (floor h)) dY.v) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d))))))) 1/2) (log (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 h) dY.v) (floor h)) dY.v) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d))))))) (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 h) dY.v) (floor h)) dY.v) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d)))))) (+ (+ (* (* (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.w dX.w) (* (floor d) (floor d))) (* (* (floor h) (floor h)) (* dX.v dX.v))) (* (* (floor h) (floor h)) (* dX.v dX.v)) (* (floor h) (floor h)) (* dX.v dX.v) (+ (* (* (* (floor h) dY.v) (floor h)) dY.v) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d))))) (* (* (floor h) dY.v) (floor h)) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* dY.w dY.w) (* (floor d) (floor d)))) (* (* dY.w dY.w) (* (floor d) (floor d))) 1/2 (log2 (sqrt (fmax (+ (+ (exp (+ (* 2 (log (neg (floor w)))) (* 2 (log 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 (+ (+ (exp (+ (* 2 (log (neg (floor w)))) (* 2 (log 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 (+ (+ (exp (+ (* 2 (log (neg (floor w)))) (* 2 (log 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)))) (+ (+ (exp (+ (* 2 (log (neg (floor w)))) (* 2 (log dX.u)))) (* (* (floor h) dX.v) (* (floor h) dX.v))) (* (* (floor d) dX.w) (* (floor d) dX.w))) (+ (exp (+ (* 2 (log (neg (floor w)))) (* 2 (log dX.u)))) (* (* (floor h) dX.v) (* (floor h) dX.v))) (exp (+ (* 2 (log (neg (floor w)))) (* 2 (log dX.u)))) (+ (* 2 (log (neg (floor w)))) (* 2 (log dX.u))) (log (neg (floor w))) (neg (floor w)) (* 2 (log dX.u)) (log dX.u) (* (* (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))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))) (* (* (floor w) dY.u) (* (floor w) dY.u)))
282.0ms
c
@0
((* c (log (+ 1 (* (- (exp x) 1) y)))) c (log (+ 1 (* (- (exp x) 1) y))) (* (- (exp x) 1) y) (- (exp x) 1) x y (* c (log (+ 1 (* (- (pow (E) x) 1) y)))) (log (+ 1 (* (- (pow (E) x) 1) y))) (* y x) (* c (log (+ 1 (* (- (pow (E) x) 1) y)))) (* (* c y) (- (exp (* x 1)) 1)) (* c y) (- (exp (* x 1)) 1) (* x 1) 1 (* c (log (+ 1 (* (- (pow (E) x) 1) y)))) (* (log (* (/ 1 (/ -1 y)) (neg (- (exp (* x 1)) 1)))) c) (+ (* (log (* y x)) c) (* (* x c) 1/2)) (log (* y x)) (* (* x c) 1/2) (* x c) 1/2 (* c (log (+ 1 (* (exp (- (log (- (exp (+ x x)) 1)) (log (+ (exp x) 1)))) y)))) (log (+ 1 (* (exp (- (log (- (exp (+ x x)) 1)) (log (+ (exp x) 1)))) y))) (+ 1 (* (exp (- (log (- (exp (+ x x)) 1)) (log (+ (exp x) 1)))) y)) (* (exp (- (log (- (exp (+ x x)) 1)) (log (+ (exp x) 1)))) y) (exp (- (log (- (exp (+ x x)) 1)) (log (+ (exp x) 1)))) (- (log (- (exp (+ x x)) 1)) (log (+ (exp x) 1))) (log (- (exp (+ x x)) 1)) (- (exp (+ x x)) 1) (+ x x) (log (+ (exp x) 1)) (+ (exp x) 1) (exp x))
227.0ms
alpha
@0
((neg (* (* (log (- 1 u0)) alpha) alpha)) (* (* (log (- 1 u0)) alpha) alpha) (* (log (- 1 u0)) alpha) (* (+ (* (+ (* (+ (* (* u0 alpha) -1/4) (* -1/3 alpha)) u0) (* -1/2 alpha)) u0) (neg alpha)) u0) (+ (* (+ (* (+ (* (* u0 alpha) -1/4) (* -1/3 alpha)) u0) (* -1/2 alpha)) u0) (neg alpha)) (+ (* (+ (* (* u0 alpha) -1/4) (* -1/3 alpha)) u0) (* -1/2 alpha)) (+ (* (* u0 alpha) -1/4) (* -1/3 alpha)) (* u0 alpha) u0 alpha -1/4 (* -1/3 alpha) -1/3 (* -1/2 alpha) -1/2 (neg alpha) (* (* (neg alpha) alpha) (log (- 1 u0))) (* alpha (* u0 alpha)) (neg (* (* (log (- 1 u0)) alpha) alpha)) (* (* (log (- 1 u0)) alpha) alpha) (* (+ (* (neg alpha) alpha) (* (* (* alpha alpha) -1/2) u0)) u0) (+ (* (neg alpha) alpha) (* (* (* alpha alpha) -1/2) u0)) (* (* (* alpha alpha) -1/2) u0) (* (* alpha alpha) -1/2) (* alpha alpha) (* (* (neg alpha) alpha) (log (- 1 u0))) (* (+ (* alpha alpha) (* (+ (* 1/3 (* (* alpha alpha) u0)) (* 1/2 (* alpha alpha))) u0)) u0) (+ (* alpha alpha) (* (+ (* 1/3 (* (* alpha alpha) u0)) (* 1/2 (* alpha alpha))) u0)) (* (+ (* 1/3 (* (* alpha alpha) u0)) (* 1/2 (* alpha alpha))) u0) (+ (* 1/3 (* (* alpha alpha) u0)) (* 1/2 (* alpha alpha))) 1/3 (* (* alpha alpha) u0) (* 1/2 (* alpha alpha)) 1/2 (neg (* (* (- (log (- 1 (* (* u0 u0) u0))) (log (+ 1 (+ (* u0 u0) (* 1 u0))))) alpha) alpha)) (* (* (- (log (- 1 (* (* u0 u0) u0))) (log (+ 1 (+ (* u0 u0) (* 1 u0))))) alpha) alpha) (* (- (log (- 1 (* (* u0 u0) u0))) (log (+ 1 (+ (* u0 u0) (* 1 u0))))) alpha) (- (log (- 1 (* (* u0 u0) u0))) (log (+ 1 (+ (* u0 u0) (* 1 u0))))) (log (- 1 (* (* u0 u0) u0))) (- 1 (* (* u0 u0) u0)) 1 (* (* u0 u0) u0) (* u0 u0) (log (+ 1 (+ (* u0 u0) (* 1 u0)))) (+ 1 (+ (* u0 u0) (* 1 u0))) (+ (* u0 u0) (* 1 u0)) (* 1 u0))

rewrite34.3s (6.7%)

Memory
-125.2MiB live, 37 782.5MiB allocated; 13.5s collecting garbage
Stop Event
299×iter-limit
139×node-limit
Counts
26 904 → 69 202

analyze29.1s (5.7%)

Memory
199.4MiB live, 37 624.1MiB allocated; 11.5s 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)

regimes24.8s (4.8%)

Memory
424.2MiB live, 37 070.1MiB allocated; 7.3s collecting garbage
Counts
10 707 → 477
Calls

158 calls:

1.8s
maxCos
1.2s
(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x (PI.f32)) tau)) (*.f32 (*.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))
720.0ms
ux
686.0ms
(*.f32 uy #s(literal 2 binary32))
668.0ms
uy
Compiler

Compiled 17 559 to 16 070 computations (8.5% saved)

derivations12.3s (2.4%)

Memory
-77.5MiB live, 11 653.8MiB allocated; 2.5s collecting garbage
Stop Event
32×fuel
3×done
Compiler

Compiled 25 300 to 3 780 computations (85.1% saved)

eval11.3s (2.2%)

Memory
500.9MiB live, 18 365.5MiB allocated; 3.4s collecting garbage
Compiler

Compiled 8 140 027 to 442 350 computations (94.6% saved)

prune8.2s (1.6%)

Memory
194.3MiB live, 11 784.2MiB allocated; 3.4s collecting garbage
Counts
67 814 → 4 055
Compiler

Compiled 532 845 to 210 467 computations (60.5% saved)

preprocess7.8s (1.5%)

Memory
-327.8MiB live, 9 370.4MiB allocated; 3.6s collecting garbage
Stop Event
36×node-limit
Compiler

Compiled 90 364 to 36 258 computations (59.9% saved)

bsearch939.0ms (0.2%)

Memory
-7.5MiB live, 1 329.7MiB allocated; 132ms collecting garbage
Algorithm
98×binary-search
39×left-value
Stop Event
93×narrow-enough
5×predicate-same
Samples
337.0ms2 231×0valid
182.0ms1 016×1valid
37.0ms161×2valid
20.0ms123×1invalid
11.0ms218×0invalid
Compiler

Compiled 42 331 to 26 759 computations (36.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 480.0ms
ival-exp: 90.0ms (18.7% of total)
ival-pow2: 62.0ms (12.9% of total)
ival-fmin: 51.0ms (10.6% of total)
ival-cos: 47.0ms (9.8% of total)
ival-mult!: 47.0ms (9.8% of total)
ival-fmax: 31.0ms (6.5% of total)
adjust: 29.0ms (6% of total)
ival-sub!: 29.0ms (6% of total)
ival-sin: 23.0ms (4.8% of total)
ival-add!: 18.0ms (3.7% of total)
ival-sqrt: 18.0ms (3.7% of total)
ival-log1p: 18.0ms (3.7% of total)
ival-fabs: 12.0ms (2.5% of total)
ival-neg: 3.0ms (0.6% of total)

start37.0ms (0%)

Memory
6.8MiB live, 62.7MiB allocated; 23ms collecting garbage

end0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Calls

1 calls:

TimeVariablePointExpression
2.4min
u1
@0
((/ 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)))) u0) (- 1 u0))))) 1 (sqrt (+ 1 (/ (* (/ 1 (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)))) u0) (- 1 u0)))) (+ 1 (/ (* (/ 1 (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)))) u0) (- 1 u0))) (/ (* (/ 1 (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)))) u0) (- 1 u0)) (* (/ 1 (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)))) u0) (/ 1 (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay)))) (+ (* (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax))) (/ (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2) (* alphay alphay))) (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (atan (* (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 (/ (cos (atan (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) (* alphax alphax)) (* 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))) 2 (* 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))))) (/ 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) (+ (/ (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 (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)) (/ 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))))) (+ (* u0 (- (* (+ (* (pow (+ (/ (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))) -2) 1/4) (* -1/2 (- (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4)))) u0) (/ 1/2 (+ (/ (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) (- (* (+ (* (pow (+ (/ (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))) -2) 1/4) (* -1/2 (- (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4)))) u0) (/ 1/2 (+ (/ (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 (+ (/ (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))) -2) 1/4) (* -1/2 (- (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4)))) u0) (+ (* (pow (+ (/ (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))) -2) 1/4) (* -1/2 (- (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4)))) (pow (+ (/ (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))) -2) -2 1/4 (* -1/2 (- (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4))) -1/2 (- (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4)) (/ 1 (+ (/ (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 (+ (/ (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))) -2) 1/4) (/ 1/2 (+ (/ (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)))))

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