Metrics for Herbie run

Date:	Saturday, May 10th, 2025
Commit:	363acd86 on unsound-last
Seed:	2025130
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:	3 589 983.4 MB

sample23.2min (27.9%)

Memory

14 515.8MiB live, 1 065 934.2MiB allocated; 6.7min collecting garbage

Samples

8.8min	3 919 062×	0	valid
3.1min	449 945×	1	valid
1.9min	11 505×	3	exit
1.6min	141 911×	2	valid
55.1s	320 496×	0	invalid
47.2s	39 706×	5	exit
24.4s	4 539×	4	exit
16.5s	15 144×	3	valid
11.0s	50 739×	0	exit
9.7s	29 217×	1	invalid
860.0ms	6 604×	1	exit
592.0ms	1 474×	2	invalid
96.0ms	46×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 13.2min

ival-mult!: 2.6min (19.7% of total)

adjust: 1.0min (7.9% of total)

ival-div!: 57.3s (7.2% of total)

ival-log: 56.4s (7.1% of total)

ival-pow: 54.5s (6.9% of total)

ival-cos: 54.2s (6.9% of total)

ival-exp: 51.7s (6.5% of total)

ival-sin: 50.0s (6.3% of total)

ival-add!: 48.1s (6.1% of total)

ival-pow2: 41.5s (5.2% of total)

ival-sub!: 38.9s (4.9% of total)

ival-sqrt: 28.7s (3.6% of total)

ival-tan: 20.7s (2.6% of total)

ival-neg: 12.0s (1.5% of total)

ival-sinu: 7.3s (0.9% of total)

ival-cosu: 7.0s (0.9% of total)

ival-hypot: 6.4s (0.8% of total)

ival-fabs: 5.6s (0.7% of total)

ival-acos: 2.9s (0.4% of total)

ival-expm1: 2.8s (0.4% of total)

ival-fmax: 2.7s (0.3% of total)

ival-log1p: 2.7s (0.3% of total)

ival-atan2: 2.6s (0.3% of total)

ival-floor: 2.4s (0.3% of total)

ival-asin: 1.9s (0.2% of total)

ival-fmod: 1.9s (0.2% of total)

ival-sinh: 1.7s (0.2% of total)

ival-atan: 1.5s (0.2% of total)

ival-if: 1.1s (0.1% of total)

ival-<=: 1.1s (0.1% of total)

ival-fmin: 941.0ms (0.1% of total)

ival-<: 904.0ms (0.1% of total)

ival-and: 747.0ms (0.1% of total)

ival-acosh: 731.0ms (0.1% of total)

ival-tanu: 672.0ms (0.1% of total)

ival-cbrt: 633.0ms (0.1% of total)

ival-cosh: 565.0ms (0.1% of total)

ival-asinh: 471.0ms (0.1% of total)

ival->: 329.0ms (0% of total)

ival-atanh: 212.0ms (0% of total)

ival-log2: 195.0ms (0% of total)

ival->=: 145.0ms (0% of total)

ival-tanh: 118.0ms (0% of total)

ival-assert: 112.0ms (0% of total)

ival-or: 15.0ms (0% of total)

ival-==: 9.0ms (0% of total)

const: 3.0ms (0% of total)

ival-pi: 1.0ms (0% of total)

exact: 0.0ms (0% of total)

Bogosity

rewrite20.8min (25%)

Memory

12 870.3MiB live, 841 212.2MiB allocated; 4.7min collecting garbage

Stop Event

6 090×	iter-limit
1 787×	node-limit
104×	unsound
55×	saturated

Counts

297 590 → 1 668 916

derivations11.8min (14.1%)

Memory

-3 379.6MiB live, 239 846.5MiB allocated; 1.3min collecting garbage

Stop Event

337×	fuel
210×	done

Compiler

Compiled 81 452 to 43 137 computations (47% saved)

eval7.0min (8.4%)

Memory: 508.8MiB live, 389 862.0MiB allocated; 2.1min collecting garbage
Compiler: Compiled 26 326 229 to 5 951 924 computations (77.4% saved)

series6.1min (7.3%)

Memory

7 499.0MiB live, 332 993.8MiB allocated; 1.8min collecting garbage

Counts

47 268 → 250 322

Calls

16107 calls:

Time	Variable		Point	Expression
13.2s	t	@	0	((fabs (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* (cos t) (tanh (asinh (/ eh (* (tan t) ew))))) eh))) (+ (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* (* (cos t) (tanh (asinh (/ eh (* (tan t) ew))))) eh)) (* (* ew (sin t)) (cos (atan (/ (/ eh ew) (tan t))))) (* ew (sin t)) ew (sin t) t (cos (atan (/ (/ eh ew) (tan t)))) (atan (/ (/ eh ew) (tan t))) (/ (/ eh ew) (tan t)) (/ eh ew) eh (tan t) (* (* (cos t) (tanh (asinh (/ eh (* (tan t) ew))))) eh) (* (cos t) (tanh (asinh (/ eh (* (tan t) ew))))) (cos t) (tanh (asinh (/ eh (* (tan t) ew)))) (asinh (/ eh (* (tan t) ew))) (/ eh (* (tan t) ew)) (* (tan t) ew) (fabs (+ (* (* (cos t) eh) (tanh (asinh (/ eh (* (tan t) ew))))) (/ (* (sin t) ew) (cosh (asinh (/ eh (* (tan t) ew))))))) (+ (* (* (cos t) eh) (tanh (asinh (/ eh (* (tan t) ew))))) (/ (* (sin t) ew) (cosh (asinh (/ eh (* (tan t) ew)))))) (* eh (tanh (log (* (* 2 (/ eh ew)) (/ 1 t))))) (tanh (log (* (* 2 (/ eh ew)) (/ 1 t)))) (log (* (* 2 (/ eh ew)) (/ 1 t))) (* (* 2 (/ eh ew)) (/ 1 t)) (* 2 (/ eh ew)) 2 (/ 1 t) 1 (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 (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) eh) (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh)) (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh) (/ (tan (neg (+ (/ (PI) 2) t))) ew) (tan (neg (+ (/ (PI) 2) t))) (neg (+ (/ (PI) 2) t)) (+ (/ (PI) 2) 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 (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (* (cos t) eh)) (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh)) (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh) (/ (tan (neg (+ (/ (PI) 2) t))) ew) (tan (neg (+ (/ (PI) 2) t))) (neg (+ (/ (PI) 2) t)) (+ (/ (PI) 2) t) (/ (PI) 2) (PI) (* (cos t) eh) (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 (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (cos t)) (/ eh ew)) (/ (sin t) (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))))) ew) (+ (* (* (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (cos t)) (/ eh ew)) (/ (sin t) (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))))) (* (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (cos t)) (/ (sin t) (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh)))) (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))))
8.6s	t	@	0	((fabs (+ (* (* (cos t) eh) (tanh (asinh (/ eh (* (tan t) ew))))) (/ (* (sin t) ew) (cosh (asinh (/ eh (* (tan t) ew))))))) (+ (* (* (cos t) eh) (tanh (asinh (/ eh (* (tan t) ew))))) (/ (* (sin t) ew) (cosh (asinh (/ eh (* (tan t) ew)))))) (* (cos t) eh) (cos t) t eh (tanh (asinh (/ eh (* (tan t) ew)))) (asinh (/ eh (* (tan t) ew))) (/ eh (* (tan t) ew)) (* (tan t) ew) (tan t) ew (/ (* (sin t) ew) (cosh (asinh (/ eh (* (tan t) ew))))) (* (sin t) ew) (sin t) (cosh (asinh (/ eh (* (tan 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)))))) (* (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) eh) (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh)) (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh) (/ (tan (neg (+ (/ (PI) 2) t))) ew) (tan (neg (+ (/ (PI) 2) t))) (neg (+ (/ (PI) 2) t)) (+ (/ (PI) 2) t) (/ (PI) 2) (PI) 2 (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)))))) (* (+ (* (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (cos t)) (/ (* (sin t) ew) (* (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) eh))) eh) (+ (* (tanh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (cos t)) (/ (* (sin t) ew) (* (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) eh))) (/ (* (sin t) ew) (* (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) eh)) (* (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) eh) (cosh (asinh (* (/ (tan (neg (+ (/ (PI) 2) t))) ew) eh))) (* (sqrt (/ (- (* (sin t) ew) (* (* (neg (cos t)) eh) (/ eh (* (tan t) ew)))) (cosh (asinh (/ eh (* (tan t) ew)))))) (sqrt (/ (- (* (sin t) ew) (* (* (neg (cos t)) eh) (/ eh (* (tan t) ew)))) (cosh (asinh (/ eh (* (tan t) ew))))))) (sqrt (/ (- (* (sin t) ew) (* (* (neg (cos t)) eh) (/ eh (* (tan t) ew)))) (cosh (asinh (/ eh (* (tan t) ew)))))) (/ (- (* (sin t) ew) (* (* (neg (cos t)) eh) (/ eh (* (tan t) ew)))) (cosh (asinh (/ eh (* (tan t) ew))))) (- (* (sin t) ew) (* (* (neg (cos t)) eh) (/ eh (* (tan t) ew)))) (* (* (neg (cos t)) eh) (/ eh (* (tan t) ew))) (* (neg (cos t)) eh) (neg (cos t)))
1.6s	x	@	inf	((* (cos x) (pow (pow (exp 5) (neg (fabs x))) (* (fabs x) -2))) (cos x) x (pow (pow (exp 5) (neg (fabs x))) (* (fabs x) -2)) (pow (exp 5) (neg (fabs x))) (exp 5) 5 (neg (fabs x)) (fabs x) (* (fabs x) -2) -2 (* (cos x) (/ 1 (exp (* -10 (* x x))))) (+ (* -19/2 (* x x)) 1) -19/2 (* x x) 1 (* (sin (neg (+ (/ (PI) -2) x))) (/ 1 (exp (* -10 (* x x))))) (sin (neg (+ (/ (PI) -2) x))) (neg (+ (/ (PI) -2) x)) (+ (/ (PI) -2) x) (/ (PI) -2) (PI) (/ 1 (exp (* -10 (* x x)))) (exp (* -10 (* x x))) (* -10 (* x x)) -10 (* (cos (+ (+ (PI) x) (PI))) (pow (exp x) (* 10 x))) (cos (+ (+ (PI) x) (PI))) (+ (+ (PI) x) (PI)) (+ (PI) x) (pow (exp x) (* 10 x)) (exp x) (* 10 x) 10 (* (cos x) (pow (pow (/ 1 (E)) (* -10 (fabs x))) (fabs x))) (pow (pow (/ 1 (E)) (* -10 (fabs x))) (fabs x)) (pow (/ 1 (E)) (* -10 (fabs x))) (/ 1 (E)) (E) (* -10 (fabs x)))
1.4s	h	@	inf	((* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))) (/ c0 (* 2 w)) c0 (* 2 w) 2 w (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))) (/ (* 2 (* (* c0 d) d)) (* (* (* h w) D) D)) (* 2 (* (* c0 d) d)) (* (* c0 d) d) (* c0 d) d (* (* (* h w) D) D) (* (* h w) D) (* h w) h D (/ (* c0 (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))) (+ w w)) (* c0 (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))) (* (sqrt -1) M) (sqrt -1) -1 M (+ w w) (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))) (* (/ (* (* c0 c0) (* 0 (/ (* d d) (* (* (* h w) D) D)))) w) -1/2) (/ (* (* c0 c0) (* 0 (/ (* d d) (* (* (* h w) D) D)))) w) (* (* c0 c0) (* 0 (/ (* d d) (* (* (* h w) D) D)))) (* c0 c0) (* 0 (/ (* d d) (* (* (* h w) D) D))) 0 (/ (* d d) (* (* (* h w) D) D)) (* d d) -1/2 (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))) (/ (/ (* (* (* d d) c0) 2) (* (* h w) D)) D) (/ (* (* (* d d) c0) 2) (* (* h w) D)) (* (* (* d d) c0) 2) (* (* d d) c0) (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))) (/ (* c0 (* d d)) (* (* w h) (* D D))) (* c0 (* d d)) (* (* w h) (* D D)) (* w h) (* D D) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))) (* c0 (* d (/ d (* (* (* D D) h) w)))) (* d (/ d (* (* (* D D) h) w))) (/ d (* (* (* D D) h) w)) (* (* (* D D) h) w) (* (* D D) h))
1.0s	cos2phi	@	0	((/ (neg (log (+ 1 (neg u0)))) (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay)))) (neg (log (+ 1 (neg u0)))) (log (+ 1 (neg u0))) (neg u0) u0 (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay))) (/ (+ (* (* alphay alphay) (/ cos2phi (* alphax alphax))) sin2phi) (* alphay alphay)) (+ (* (* alphay alphay) (/ cos2phi (* alphax alphax))) sin2phi) (* alphay alphay) alphay (/ cos2phi (* alphax alphax)) cos2phi (* alphax alphax) alphax sin2phi (/ (neg (log (- 1 u0))) (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay)))) (* (* alphax alphax) (/ (neg (log (- 1 u0))) cos2phi)) (/ (* alphax (* alphax u0)) cos2phi) (* alphax (* alphax u0)) (* alphax u0) (/ (neg (log (- 1 u0))) (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay)))) (neg (log (- 1 u0))) (log (- 1 u0)) (- 1 u0) 1 (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay))) (/ (/ sin2phi alphay) alphay) (/ sin2phi alphay) (/ (neg (log (- 1 u0))) (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay)))) (/ (* (* (* alphax alphax) alphay) u0) (+ (* alphay cos2phi) (/ (* (* alphax alphax) sin2phi) alphay))) (* (* (* alphax alphax) alphay) u0) (* (* alphax alphax) alphay) (+ (* alphay cos2phi) (/ (* (* alphax alphax) sin2phi) alphay)) (/ (* (* alphax alphax) sin2phi) alphay) (* (* alphax alphax) sin2phi) (/ (neg (log (- 1 u0))) (+ (/ cos2phi (* alphax alphax)) (/ sin2phi (* alphay alphay)))) (* (* alphax alphax) (/ (neg (log (- 1 u0))) cos2phi)) (* (+ (* (/ (+ (* 1/2 (* alphax alphax)) (* 1/3 (* (* alphax alphax) u0))) cos2phi) u0) (/ (* alphax alphax) cos2phi)) u0) (+ (* (/ (+ (* 1/2 (* alphax alphax)) (* 1/3 (* (* alphax alphax) u0))) cos2phi) u0) (/ (* alphax alphax) cos2phi)) (/ (+ (* 1/2 (* alphax alphax)) (* 1/3 (* (* alphax alphax) u0))) cos2phi) (+ (* 1/2 (* alphax alphax)) (* 1/3 (* (* alphax alphax) u0))) 1/2 (* 1/3 (* (* alphax alphax) u0)) 1/3 (* (* alphax alphax) u0) (/ (* alphax alphax) cos2phi))

regimes5.2min (6.2%)

Memory

484.6MiB live, 259 369.3MiB allocated; 1.2min collecting garbage

Counts

110 351 → 9 558

Calls

1 231 calls:

25.5s	x
19.4s	(+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
18.2s	y
11.7s	z
8.9s	a

Compiler

Compiled 105 785 to 126 162 computations (-19.3% saved)

preprocess3.1min (3.7%)

Memory

-703.9MiB live, 136 237.5MiB allocated; 38.1s collecting garbage

Stop Event

499×	node-limit
49×	saturated
1×	iter-limit

Compiler

Compiled 607 579 to 404 797 computations (33.4% saved)

prune2.8min (3.3%)

Memory: -1 541.2MiB live, 158 154.6MiB allocated; 30.8s collecting garbage
Counts: 1 511 152 → 35 958
Compiler: Compiled 2 177 757 to 1 538 929 computations (29.3% saved)

analyze2.1min (2.5%)

Memory

912.5MiB live, 101 367.6MiB allocated; 36.1s collecting garbage

Algorithm

552×	search
2×	random

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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)

bsearch1.2min (1.5%)

Memory

-83.6MiB live, 64 855.2MiB allocated; 14.5s collecting garbage

Algorithm

3 124×	binary-search
1 944×	left-value

Stop Event

3 047×	narrow-enough
70×	predicate-same
7×	predicate-failed

Samples

28.2s	209 203×	0	valid
13.4s	19 703×	1	valid
1.1s	2 470×	2	valid
989.0ms	9 645×	0	invalid
118.0ms	101×	5	exit
100.0ms	78×	3	valid
38.0ms	154×	1	invalid
20.0ms	241×	0	exit
6.0ms	2×	4	valid
2.0ms	19×	1	exit
2.0ms	7×	2	invalid

Compiler

Compiled 1 314 327 to 1 195 008 computations (9.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.1s

ival-mult!: 8.3s (27.7% of total)

ival-cos: 3.9s (12.8% of total)

ival-sin: 3.8s (12.6% of total)

ival-sub!: 2.3s (7.8% of total)

ival-add!: 1.9s (6.4% of total)

ival-div!: 1.8s (6% of total)

adjust: 1.8s (6% of total)

ival-pow: 1.0s (3.3% of total)

ival-log: 994.0ms (3.3% of total)

ival-pow2: 869.0ms (2.9% of total)

ival-sqrt: 574.0ms (1.9% of total)

ival-exp: 469.0ms (1.6% of total)

ival-neg: 415.0ms (1.4% of total)

ival-sinu: 343.0ms (1.1% of total)

ival-atan2: 315.0ms (1% of total)

ival-tan: 272.0ms (0.9% of total)

ival-hypot: 251.0ms (0.8% of total)

ival-cosu: 172.0ms (0.6% of total)

ival-fmax: 157.0ms (0.5% of total)

ival->=: 87.0ms (0.3% of total)

ival-acos: 74.0ms (0.2% of total)

ival-log1p: 59.0ms (0.2% of total)

ival-fabs: 35.0ms (0.1% of total)

ival-expm1: 35.0ms (0.1% of total)

ival-atan: 32.0ms (0.1% of total)

ival-if: 16.0ms (0.1% of total)

ival-fmin: 14.0ms (0% of total)

ival-tanh: 14.0ms (0% of total)

ival-asin: 13.0ms (0% of total)

ival-cbrt: 12.0ms (0% of total)

ival-fmod: 11.0ms (0% of total)

ival-tanu: 9.0ms (0% of total)

ival-cosh: 7.0ms (0% of total)

start56.0ms (0%)

Memory: 43.0MiB live, 140.5MiB allocated; 19ms collecting garbage

end4.0ms (0%)

Memory

10.5MiB live, 10.1MiB allocated; 0ms collecting garbage

Calls

1 calls:

Time	Variable		Point	Expression
2.3min	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 (/ u0 (* (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (- 1 u0)))) (/ u0 (* (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (- 1 u0))) u0 (* (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (- 1 u0)) (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI))))))) (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))) (/ alphay alphax) alphay alphax (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI))))) (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))) 1/2 (PI) (* 2 (* u1 (PI))) 2 (* u1 (PI)) u1 (* alphax alphax) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay)) (* alphay alphay) (- 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 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (- 1 u0)))) 1) (* (* alphay alphay) (/ u0 (- 1 u0))) (/ u0 (- 1 u0)) (sqrt (/ 1 (+ (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) 1))) (/ 1 (+ (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) 1)) (+ (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) 1) (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0)) (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2))) (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax))) (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 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))))) (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 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (- 1 u0)))) 1) (/ u0 (* (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (- 1 u0))) (* (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (- 1 u0)) (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2))) (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2) (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) (tan (* (PI) (+ (* 2 u1) 1/2))) (* (PI) (+ (* 2 u1) 1/2)) (+ (* 2 u1) 1/2) (- 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)))) (+ (* (/ u0 (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax))))) 1/2) 1) (/ u0 (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax))))) (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax))) (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))

Time

Variable

Point

Expression

2.3min

u1

((/ 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 (/ u0 (* (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (- 1 u0)))) (/ u0 (* (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (- 1 u0))) u0 (* (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (- 1 u0)) (+ (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay))) (/ (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (* alphax alphax)) (- 1 (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2)) (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI))))))) (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))) (/ alphay alphax) alphay alphax (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI))))) (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))) 1/2 (PI) (* 2 (* u1 (PI))) 2 (* u1 (PI)) u1 (* alphax alphax) (/ (pow (tanh (asinh (* (/ alphay alphax) (tan (+ (* 1/2 (PI)) (* 2 (* u1 (PI)))))))) 2) (* alphay alphay)) (* alphay alphay) (- 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 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (- 1 u0)))) 1) (* (* alphay alphay) (/ u0 (- 1 u0))) (/ u0 (- 1 u0)) (sqrt (/ 1 (+ (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) 1))) (/ 1 (+ (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) 1)) (+ (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) 1) (/ u0 (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0))) (* (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (- 1 u0)) (+ (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax)))) (/ (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (* alphay alphay)) (- 1 (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)))) (/ 1 (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2))) (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (/ 1 (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 1/2))) (/ alphay alphax)) 2)) (* alphax alphax))) (* (+ 1 (pow (* (tan (* (PI) (+ (* 2 u1) 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))))) (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 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