Herbie run

Date:Friday, May 16th, 2025
Commit:7acd8706 on new-rules
Seed:2025136
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:2 963 785.9 MB

Time bar (total: 42.6min)

sample17.2min (40.5%)

Memory
13 426.1MiB live, 1 163 989.5MiB allocated; 6.9min collecting garbage
Samples
5.9min3 920 713×0valid
2.1min17 568×3exit
2.0min449 384×1valid
1.1min141 405×2valid
39.4s323 617×0invalid
38.9s39 658×5exit
19.8s4 469×4exit
13.9s15 478×3valid
6.8s29 146×1invalid
6.7s49 927×0exit
827.0ms6 642×1exit
471.0ms1 523×2invalid
89.0ms39×4valid
2.0ms2×2exit
Precisions
Click to see histograms. Total time spent on operations: 9.7min
ival-mult!: 1.7min (17.3% of total)
adjust: 58.6s (10.1% of total)
ival-exp: 44.5s (7.7% of total)
ival-div!: 44.0s (7.6% of total)
ival-pow: 42.5s (7.3% of total)
ival-log: 41.8s (7.2% of total)
ival-sub!: 33.6s (5.8% of total)
ival-pow2: 31.2s (5.4% of total)
ival-add!: 29.1s (5% of total)
ival-cos: 29.0s (5% of total)
ival-sin: 25.2s (4.4% of total)
ival-sqrt: 22.9s (3.9% of total)
ival-tan: 17.8s (3.1% of total)
ival-neg: 9.8s (1.7% of total)
ival-sinu: 6.9s (1.2% of total)
ival-cosu: 6.8s (1.2% of total)
ival-fabs: 5.3s (0.9% of total)
ival-hypot: 4.1s (0.7% of total)
ival-fmax: 3.2s (0.5% of total)
ival-atan2: 2.4s (0.4% of total)
ival-expm1: 2.4s (0.4% of total)
ival-log1p: 2.0s (0.3% of total)
ival-asin: 1.9s (0.3% of total)
ival-acos: 1.9s (0.3% of total)
ival-sinh: 1.7s (0.3% of total)
ival-atan: 1.5s (0.3% of total)
ival-fmod: 1.4s (0.2% of total)
ival-<=: 1.0s (0.2% of total)
ival-fmin: 970.0ms (0.2% of total)
ival-floor: 807.0ms (0.1% of total)
ival-and: 708.0ms (0.1% of total)
ival-<: 666.0ms (0.1% of total)
ival-cbrt: 629.0ms (0.1% of total)
ival-atanh: 403.0ms (0.1% of total)
ival-if: 370.0ms (0.1% of total)
ival-asinh: 346.0ms (0.1% of total)
ival-log2: 294.0ms (0.1% of total)
ival-cosh: 276.0ms (0% of total)
ival-acosh: 238.0ms (0% of total)
ival-tanu: 190.0ms (0% of total)
ival-assert: 110.0ms (0% of total)
ival-tanh: 99.0ms (0% of total)
ival->: 77.0ms (0% of total)
ival->=: 44.0ms (0% of total)
ival-or: 14.0ms (0% of total)
ival-==: 3.0ms (0% of total)
const: 2.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-pi: 0.0ms (0% of total)
Bogosity

rewrite7.0min (16.6%)

Memory
9 917.1MiB live, 472 514.2MiB allocated; 2.1min collecting garbage
Stop Event
4 557×iter-limit
1 842×node-limit
123×unsound
36×saturated
Counts
256 205 → 616 490

series5.3min (12.5%)

Memory
8 146.2MiB live, 396 354.0MiB allocated; 2.1min collecting garbage
Counts
50 315 → 205 890
Calls

16521 calls:

TimeVariablePointExpression
2.7s
t
@0
((fabs (+ (* ew (* (sin t) (/ 1 (sqrt (+ 1 (pow (/ eh (* ew (tan t))) 2)))))) (* (* (cos t) eh) (tanh (asinh (/ eh (* ew (tan t)))))))) (+ (* ew (* (sin t) (/ 1 (sqrt (+ 1 (pow (/ eh (* ew (tan t))) 2)))))) (* (* (cos t) eh) (tanh (asinh (/ eh (* ew (tan t))))))) ew (* (sin t) (/ 1 (sqrt (+ 1 (pow (/ eh (* ew (tan t))) 2))))) (sin t) t (/ 1 (sqrt (+ 1 (pow (/ eh (* ew (tan t))) 2)))) 1 (sqrt (+ 1 (pow (/ eh (* ew (tan t))) 2))) (+ 1 (pow (/ eh (* ew (tan t))) 2)) (pow (/ eh (* ew (tan t))) 2) (/ eh (* ew (tan t))) eh (* ew (tan t)) (tan t) 2 (* (* (cos t) eh) (tanh (asinh (/ eh (* ew (tan t)))))) (* (cos t) eh) (cos t) (tanh (asinh (/ eh (* ew (tan t))))) (asinh (/ eh (* ew (tan t)))) (fabs (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t))))))) (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t)))))) (* (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew)))) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew)))) (asinh (/ (* (cos t) eh) (* (sin t) ew))) (/ (* (cos t) eh) (* (sin t) ew)) (* (sin t) ew) (fabs (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t))))))) (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t)))))) (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t)))) (atan (/ (/ eh ew) (tan t))) (/ (/ eh ew) (tan t)) (/ eh (* t ew)) (* t ew) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t))))) (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t)))) (fabs (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t))))))) (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t)))))) (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* ew (sin t)) (sin t) (* (+ (* (* t t) -1/6) 1) t) (+ (* (* t t) -1/6) 1) (* t t) -1/6 (cos (atan (/ (/ eh ew) (tan t)))) (atan (/ (/ eh ew) (tan t))) (/ (/ eh ew) (tan t)) (/ eh ew) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t))))) (sin (atan (/ (/ eh ew) (tan t)))) (fabs (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t))))))) (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* eh (cos t)) (sin (atan (/ (/ eh ew) (tan t)))))) (neg (* (+ (neg (/ (* (* (cos t) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew))))) ew)) (neg (* (/ 1 (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)))) (sin t)))) ew)) (* (+ (neg (/ (* (* (cos t) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew))))) ew)) (neg (* (/ 1 (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)))) (sin t)))) ew) (+ (neg (/ (* (* (cos t) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew))))) ew)) (neg (* (/ 1 (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)))) (sin t)))) (neg (/ (* (* (cos t) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew))))) ew)) (/ (* (* (cos t) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew))))) ew) (* (* (cos t) eh) (tanh (asinh (/ (* (cos t) eh) (* (sin t) ew))))) (neg (* (/ 1 (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)))) (sin t))) (* (/ 1 (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)))) (sin t)) (/ 1 (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)))) (sqrt (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2))) (+ 1 (pow (/ (* (cos t) eh) (* (sin t) ew)) 2)) (pow (/ (* (cos t) eh) (* (sin t) ew)) 2))
2.2s
z
@inf
((+ (* (/ (- t z) (- t a)) y) x) (/ (- t z) (- t a)) (/ (- t z) t) (- t z) t z y x (+ x (/ (* y (- z t)) (- a t))) (+ (* y (/ z a)) x) (/ (* y z) a) (* y z) a (+ x (/ (* y (- z t)) (- a t))) (* y (/ z (- a t))) (/ z (- a t)) (/ (neg z) t) (neg z) (+ x (/ (* y (- z t)) (- a t))) (/ (* y z) (- a t)) (- a t) (+ x (/ (* y (- z t)) (- a t))) (/ (* (- z t) y) (- a t)) (* (- z t) y) (- z t))
1.0s
re
@0
((/ (neg (log (sqrt (+ (* re re) (* im im))))) (log 1/10)) (neg (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im)))) (log im) im (log 1/10) 1/10 (/ (neg (log (sqrt (+ (* re re) (* im im))))) (log 1/10)) (neg (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im)))) (log re) re (/ (neg (log (sqrt (+ (* re re) (* im im))))) (log 1/10)) (neg (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (neg im) (/ (neg (log (sqrt (+ (* re re) (* im im))))) (log 1/10)) (neg (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (neg re) (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)) (log (sqrt (+ (* re re) (* im im)))) (sqrt (+ (* re re) (* im im))) (+ (* re re) (* im im)) (* im im) (log 10) 10)
1.0s
im
@inf
((/ (atan2 im re) (log 10)) (atan2 im re) im re (log 10) 10)
1.0s
x
@0
((copysign (asinh (fabs x)) x) (asinh (fabs x)) (fabs x) x (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (log x) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (neg x) (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)) 1 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1)))) x) (log (+ (fabs x) (sqrt (+ (* x x) 1)))) (+ (fabs x) (sqrt (+ (* x x) 1))) (* (+ (/ (fabs x) x) 1) x) (+ (/ (fabs x) x) 1) (/ (fabs x) x))

regimes2.8min (6.6%)

Memory
-240.9MiB live, 224 807.1MiB allocated; 57.7s collecting garbage
Counts
88 138 → 8 697
Calls

1 235 calls:

14.2s
x
10.0s
t
9.4s
y
7.0s
z
5.9s
a
Compiler

Compiled 98 005 to 117 427 computations (-19.8% saved)

derivations2.4min (5.8%)

Memory
-341.9MiB live, 132 903.3MiB allocated; 29.7s collecting garbage
Stop Event
354×fuel
193×done
Compiler

Compiled 76 081 to 42 164 computations (44.6% saved)

eval2.1min (5%)

Memory
2 701.2MiB live, 177 563.9MiB allocated; 56.9s collecting garbage
Compiler

Compiled 14 153 426 to 3 085 962 computations (78.2% saved)

preprocess2.1min (4.8%)

Memory
-6 052.0MiB live, 131 605.1MiB allocated; 47.4s collecting garbage
Stop Event
517×node-limit
31×saturated
Compiler

Compiled 532 742 to 371 388 computations (30.3% saved)

analyze1.4min (3.3%)

Memory
1 514.0MiB live, 94 118.4MiB allocated; 34.8s collecting garbage
Algorithm
552×search
2×random
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%84.6%15.4%0%0%0%0
39.7%33.6%51.1%15.4%0%0%0%1
45.6%38.2%45.6%15.4%0%0.8%0%2
54.1%44.3%37.6%15.4%0%2.8%0%3
60.9%49.3%31.6%15.4%0%3.7%0%4
67.2%54.1%26.4%15.4%0%4.2%0%5
71.2%57%23.1%15.4%0%4.6%0%6
75.1%59.7%19.8%15.4%0%5.2%0%7
77.1%61%18.1%15.4%0%5.6%0%8
79.8%62.8%15.9%15.4%0%5.9%0%9
81.3%63.8%14.6%15.4%0%6.2%0%10
83.6%65.4%12.9%15.4%0%6.3%0%11
84.7%66.1%11.9%15.4%0%6.6%0%12
Compiler

Compiled 30 225 to 8 606 computations (71.5% saved)

prune1.1min (2.6%)

Memory
-1 178.5MiB live, 100 402.7MiB allocated; 22.8s collecting garbage
Counts
601 653 → 33 693
Compiler

Compiled 1 969 947 to 1 429 740 computations (27.4% saved)

bsearch1.0min (2.4%)

Memory
-457.1MiB live, 69 407.8MiB allocated; 23.4s collecting garbage
Algorithm
2 831×binary-search
1 672×left-value
Stop Event
2 757×narrow-enough
72×predicate-same
2×predicate-failed
Samples
21.5s198 128×0valid
7.1s16 905×1valid
3.0s539×4exit
1.2s885×5exit
1.1s2 569×2valid
746.0ms8 620×0invalid
350.0ms254×3valid
17.0ms221×0exit
11.0ms72×1invalid
Compiler

Compiled 1 264 091 to 1 156 987 computations (8.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.1s
ival-mult!: 6.0s (23.9% of total)
ival-pow: 4.1s (16.2% of total)
ival-div!: 2.4s (9.5% of total)
ival-sub!: 2.0s (8% of total)
ival-sin: 1.9s (7.5% of total)
ival-cos: 1.9s (7.5% of total)
adjust: 1.5s (5.9% of total)
ival-add!: 1.2s (4.8% of total)
ival-log: 861.0ms (3.4% of total)
ival-pow2: 668.0ms (2.7% of total)
ival-sqrt: 531.0ms (2.1% of total)
ival-exp: 495.0ms (2% of total)
ival-tan: 310.0ms (1.2% of total)
ival-sinu: 240.0ms (1% of total)
ival-cosu: 219.0ms (0.9% of total)
ival-neg: 184.0ms (0.7% of total)
ival-hypot: 173.0ms (0.7% of total)
ival-atan2: 164.0ms (0.7% of total)
ival-fmax: 70.0ms (0.3% of total)
ival-fabs: 67.0ms (0.3% of total)
ival-acos: 41.0ms (0.2% of total)
ival->=: 27.0ms (0.1% of total)
ival-tanu: 26.0ms (0.1% of total)
ival-cbrt: 23.0ms (0.1% of total)
ival-atan: 23.0ms (0.1% of total)
ival-log1p: 19.0ms (0.1% of total)
ival-fmin: 18.0ms (0.1% of total)
ival-if: 18.0ms (0.1% of total)
ival-tanh: 9.0ms (0% of total)
ival-cosh: 8.0ms (0% of total)
ival-fmod: 7.0ms (0% of total)
ival-asin: 3.0ms (0% of total)
ival-expm1: 3.0ms (0% of total)

start73.0ms (0%)

Memory
-27.7MiB live, 109.2MiB allocated; 44ms collecting garbage

end4.0ms (0%)

Memory
11.2MiB live, 10.6MiB 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))))) 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 (/ (* (/ 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 (+ (/ (* (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 (+ (/ (* (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 (+ (/ (* (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)))) (+ (/ (* (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))) (/ (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (* alphax alphax)) (* (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))))) (cos (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))))) (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))) (/ alphay alphax) alphay alphax (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI)))) (+ (* (* 2 (PI)) u1) (* 1/2 (PI))) (* (+ (* (/ (PI) u1) 1/2) (+ (PI) (PI))) u1) (+ (* (/ (PI) u1) 1/2) (+ (PI) (PI))) (/ (PI) u1) (PI) u1 1/2 (+ (PI) (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)) (* (sin (atan (* (/ alphay alphax) (tan (+ (* (* 2 (PI)) u1) (* 1/2 (PI))))))) (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))))) (/ 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))) (+ (* (* alphax alphax) (/ u0 (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))))) 1) (/ u0 (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)))) (* (- 1 u0) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))) (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (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) 1/2) 2 (/ 1 (sqrt (+ (/ 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 (+ (/ 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))) 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 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)) (/ (- 1 (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2)) (* alphax alphax)) (/ 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))))) (+ (* (* alphay alphay) (- (neg (* (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) 1/4) (/ (* (- 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)))) -1/2) (/ (* -1/4 (* u0 u0)) (* (pow (tanh 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u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) 1/4) (/ (* (- 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)))) -1/2) (/ (* -1/4 (* u0 u0)) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0))))) (* alphay alphay))) (* (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) 1/4) (/ (* (- 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)))) -1/2) (/ (* -1/4 (* u0 u0)) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0))))) (* alphay alphay)) (+ (* (+ (* (/ (* u0 u0) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) 1/4) (/ (* (- 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)))) -1/2) (/ (* -1/4 (* 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)))) 1/4) (/ (* (- 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)) 1/4 (/ (* (- 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)) -1/2 (/ (* -1/4 (* u0 u0)) (* (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 4) (* (- 1 u0) (- 1 u0)))) (* -1/4 (* u0 u0)) -1/4 (* (/ u0 (* (- 1 u0) (pow (tanh (asinh (* (tan (+ (* (+ (PI) (PI)) u1) (* (PI) 1/2))) (/ alphay alphax)))) 2))) 1/2) (/ 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)))

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