Metrics for Herbie run

Date:	Thursday, February 6th, 2025
Commit:	f63971dc on main
Seed:	2025037
Parameters:	256 points for 4 iterations
Flags:	`reduce:regimesreduce:binary-searchreduce:branch-expressionsreduce:simplifysetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default
Memory:	570 614.9 MB

sample3.6min (46%)

Memory

3 353.7MiB live, 252 287.9MiB allocated; 59.8s collecting garbage

Samples

55.7s	120 066×	1	valid
51.0s	17 822×	5	exit
38.8s	281 342×	0	valid
17.1s	24 671×	2	valid
7.8s	3 211×	3	valid
6.7s	34 675×	0	exit
3.0s	12 322×	1	invalid
2.7s	19 618×	0	invalid
499.0ms	787×	2	invalid
150.0ms	22×	4	valid
20.0ms	33×	1	exit
12.0ms	1×	2	exit

Precisions

Click to see histograms. Total time spent on operations: 2.6min

ival-pow: 41.5s (26.2% of total)

ival-mult: 17.9s (11.3% of total)

adjust: 15.7s (9.9% of total)

ival-cos: 12.5s (7.9% of total)

ival-div: 11.2s (7% of total)

ival-sin: 8.2s (5.2% of total)

ival-pow2: 7.5s (4.7% of total)

ival-add: 6.1s (3.9% of total)

ival-sub: 5.9s (3.7% of total)

ival-exp: 5.7s (3.6% of total)

ival-sinu: 5.7s (3.6% of total)

ival-cosu: 4.7s (3% of total)

ival-log: 4.3s (2.7% of total)

ival-sqrt: 3.6s (2.3% of total)

ival-neg: 2.2s (1.4% of total)

ival-log1p: 956.0ms (0.6% of total)

ival-atan2: 821.0ms (0.5% of total)

ival-hypot: 779.0ms (0.5% of total)

ival-tan: 596.0ms (0.4% of total)

const: 462.0ms (0.3% of total)

ival-acos: 362.0ms (0.2% of total)

exact: 358.0ms (0.2% of total)

ival-atan: 334.0ms (0.2% of total)

ival-cbrt: 298.0ms (0.2% of total)

ival-assert: 182.0ms (0.1% of total)

ival-asin: 144.0ms (0.1% of total)

ival-fabs: 139.0ms (0.1% of total)

ival-pi: 106.0ms (0.1% of total)

ival-<: 97.0ms (0.1% of total)

ival-and: 52.0ms (0% of total)

ival-<=: 34.0ms (0% of total)

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

ival-or: 0.0ms (0% of total)

Bogosity

rewrite53.7s (11.4%)

Memory

951.5MiB live, 64 057.4MiB allocated; 13.8s collecting garbage

Stop Event

451×	iter limit
186×	node limit
6×	unsound
4×	saturated

Counts

52 431 → 78 608

series33.1s (7%)

Memory

506.6MiB live, 43 685.8MiB allocated; 9.8s collecting garbage

Counts

7 551 → 44 880

Calls

1602 calls:

Time	Variable		Point	Expression
900.0ms	phi1	@	-inf	((* R (* 2 (atan2 (sqrt (+ (pow (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))))) R (* 2 (atan2 (sqrt (+ (pow (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))))) 2 (atan2 (sqrt (+ (pow (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))) (sqrt (+ (pow (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (+ (pow (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))) (pow (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) 2) (- (* (sin (/ phi1 2)) (cos (/ phi2 2))) (* (cos (/ phi1 2)) (sin (/ phi2 2)))) (* (sin (/ phi1 2)) (cos (/ phi2 2))) (sin (/ phi1 2)) (/ phi1 2) phi1 (cos (/ phi2 2)) (/ phi2 2) phi2 (* (cos (/ phi1 2)) (sin (/ phi2 2))) (cos (/ phi1 2)) (sin (/ phi2 2)) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))) (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (* (cos phi1) (cos phi2)) (cos phi1) (cos phi2) (sin (/ (- lambda1 lambda2) 2)) (/ (- lambda1 lambda2) 2) (- lambda1 lambda2) lambda1 lambda2 (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))) (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))) (pow (sin (/ (- phi1 phi2) 2)) 2) (sin (/ (- phi1 phi2) 2)) (/ (- phi1 phi2) 2) (- phi1 phi2) (* (* (atan2 (sqrt (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))) (sqrt (- 1 (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))))) 2) R) (* (atan2 (sqrt (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))) (sqrt (- 1 (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))))) 2) (atan2 (sqrt (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))) (sqrt (- 1 (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))))) (sqrt (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))) (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2)) (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2))))) 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))) (cos (* 2 (/ (- lambda1 lambda2) 2))) (* 2 (/ (- lambda1 lambda2) 2)) (sqrt (- 1 (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2)))) (- 1 (+ (* (* (cos phi2) (cos phi1)) (- 1/2 (* 1/2 (cos (* 2 (/ (- lambda1 lambda2) 2)))))) (pow (sin (/ (- phi1 phi2) 2)) 2))) (* R (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))))) (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))))) (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))) (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))) (+ (* (* (cos phi2) (cos phi1)) (pow (sin (* -1/2 lambda2)) 2)) (pow (sin (* 1/2 (- phi1 phi2))) 2)) (pow (sin (* -1/2 lambda2)) 2) (sin (* -1/2 lambda2)) (* -1/2 lambda2) -1/2 (pow (sin (* 1/2 (- phi1 phi2))) 2) (sin (* 1/2 (- phi1 phi2))) (* 1/2 (- phi1 phi2)) (* R (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))))) (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))))) (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))) (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))) (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))) (* (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))) (* (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (* (sin (+ (* -1 phi1) (/ (PI) 2))) (cos phi2)) (sin (+ (* -1 phi1) (/ (PI) 2))) (+ (* -1 phi1) (/ (PI) 2)) -1 (/ (PI) 2) (PI) (* R (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))))) (* 2 (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))))) (atan2 (sqrt (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))))) (sqrt (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))))) (- 1 (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))))) (+ (pow (sin (/ (- phi1 phi2) 2)) 2) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)))) (* (* (* (cos phi1) (cos phi2)) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2))) (sin (/ (- lambda1 lambda2) 2)) (+ (* (* 1/2 lambda1) (cos (* -1/2 lambda2))) (sin (* -1/2 lambda2))) (* 1/2 lambda1) (cos (* -1/2 lambda2)))
509.0ms	angle	@	0	((/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* 1/4 (* a (* x-scale 4))) (* a x-scale) a x-scale (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* 1/4 (* (* x-scale (* y-scale (sqrt 8))) (sqrt (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)))))))) 1/4 (* (* x-scale (* y-scale (sqrt 8))) (sqrt (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2))))))) (* x-scale (* y-scale (sqrt 8))) (* y-scale (sqrt 8)) y-scale (sqrt 8) 8 (sqrt (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)))))) (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2))))) (- (/ (* a a) (* y-scale y-scale)) (* -1 (/ (* a a) (* y-scale y-scale)))) (/ (* a a) (* y-scale y-scale)) (* a a) (* y-scale y-scale) (* -1 (/ (* a a) (* y-scale y-scale))) -1 (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale 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(sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))) (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2)) (* 4 (* (* b a) (* b (neg a)))) 4 (* (* b a) (* b (neg a))) (* b a) b (* b (neg a)) (neg a) (pow (* x-scale y-scale) 2) (* x-scale y-scale) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ 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(PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* 1/4 (* (* b (* x-scale (* y-scale (sqrt 8)))) (sqrt (- (+ (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) (sqrt (+ (* 4 (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2))))))) (* (* b (* x-scale (* y-scale (sqrt 8)))) (sqrt (- (+ (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) (sqrt (+ (* 4 (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2)))))) (* b (* x-scale (* y-scale (sqrt 8)))) (* x-scale (* y-scale (sqrt 8))) (* y-scale (sqrt 8)) (sqrt 8) 8 (sqrt (- (+ (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) (sqrt (+ (* 4 (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2))))) (- (+ (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) (sqrt (+ (* 4 (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2)))) (+ (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (pow (cos (* 1/180 (* angle (PI)))) 2) (cos (* 1/180 (* angle (PI)))) (* 1/180 (* angle (PI))) 1/180 (* angle (PI)) angle (PI) (* x-scale x-scale) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale)) (pow (sin (* 1/180 (* angle (PI)))) 2) (sin (* 1/180 (* angle (PI)))) (sqrt (+ (* 4 (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2))) (+ (* 4 (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2)) (/ (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (pow (* x-scale y-scale) 2)) (pow (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) 2) (* (cos (* 1/180 (* angle (PI)))) (sin (* 1/180 (* angle (PI))))) (pow (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) 2) (- (/ (pow (cos (* 1/180 (* angle (PI)))) 2) (* x-scale x-scale)) (/ (pow (sin (* 1/180 (* angle (PI)))) 2) (* y-scale y-scale))) (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2)))))) (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))) (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2)))) (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) (pow (* a (sin (* (/ angle 180) (PI)))) 2) (* a (sin (* (/ angle 180) (PI)))) (sin (* (/ angle 180) (PI))) (* (/ angle 180) (PI)) (/ angle 180) 180 (pow (* b (cos (* (/ angle 180) (PI)))) 2) (* b (cos (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI))) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale) (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) (pow (* a (cos (* (/ angle 180) (PI)))) 2) (* a (cos (* (/ angle 180) (PI)))) (pow (* b (sin (* (/ angle 180) (PI)))) 2) (* b (sin (* (/ angle 180) (PI)))) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))) (/ (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (* x-scale x-scale)) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (* a (sin (* 1/180 (* angle (PI))))) (pow (* b (cos (* 1/180 (* angle (PI))))) 2) (* b (cos (* 1/180 (* angle (PI))))) (/ (neg (sqrt (* (* (* 2 (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* b a) (* b (neg a)))) (- (+ (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* 1/4 (* (* x-scale (* y-scale (sqrt 8))) (sqrt (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)))))))) (* (* x-scale (* y-scale (sqrt 8))) (sqrt (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2))))))) (sqrt (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)))))) (- (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2))))) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)) (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (* a (cos (* 1/180 (* angle (PI))))) (pow (* b (sin (* 1/180 (* angle (PI))))) 2) (* b (sin (* 1/180 (* angle (PI))))) (* 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)))) 1/2 (/ (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2))) (+ (* -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale)))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)))) -2 (* (+ (pow (* a (sin (* 1/180 (* angle (PI))))) 2) (pow (* b (cos (* 1/180 (* angle (PI))))) 2)) (/ (+ (pow (* a (cos (* 1/180 (* angle (PI))))) 2) (pow (* b (sin (* 1/180 (* angle (PI))))) 2)) (* y-scale y-scale))) (* 4 (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale))) (/ (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (* y-scale y-scale)) (* (pow (cos (* 1/180 (* angle (PI)))) 2) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2)) (pow (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) 2) (* (sin (* 1/180 (* angle (PI)))) (- (* b b) (* a a))) (- (* b b) (* a a)) (* a a))

regimes30.4s (6.4%)

Memory

602.6MiB live, 38 982.9MiB allocated; 4.8s collecting garbage

Counts

18 186 → 893

Calls

155 calls:

2.5s	phi1
2.4s	phi2
1.9s	lambda1
1.7s	lambda2
1.5s	b

Compiler

Compiled 18 588 to 14 872 computations (20% saved)

eval25.9s (5.5%)

Memory: -158.6MiB live, 32 768.9MiB allocated; 11.0s collecting garbage
Compiler: Compiled 12 310 401 to 571 934 computations (95.4% saved)

prune24.0s (5.1%)

Memory: -116.8MiB live, 40 806.1MiB allocated; 7.0s collecting garbage
Counts: 109 837 → 5 764
Compiler: Compiled 970 564 to 364 979 computations (62.4% saved)

explain21.6s (4.6%)

Memory

-194.8MiB live, 29 014.0MiB allocated; 5.0s collecting garbage

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`#f`	sensitivity	1895	0
`+.f64`	`#f`	cancellation	1702	41
`sin.f64`	`#f`	sensitivity	1622	1
`sqrt.f64`	`#f`	oflow-rescue	1399	0
`-.f64`	`#f`	cancellation	964	13
`-.f64`	`#f`	nan-rescue	657	0
`log.f64`	`#f`	sensitivity	602	5
`/.f64`	`#f`	o/n	530	0
`/.f64`	`#f`	o/o	390	0
`/.f64`	`#f`	u/u	268	0
`*.f64`	`#f`	*no**	262	0
`/.f64`	`#f`	u/n	179	0
`sqrt.f64`	`#f`	uflow-rescue	167	0
`exp.f64`	`#f`	sensitivity	165	24
`cbrt.f64`	`#f`	oflow-rescue	101	0
`/.f64`	`#f`	n/o	95	0
`*.f64`	`#f`	*nu**	76	0
`/.f64`	`#f`	n/u	39	0
`cbrt.f64`	`#f`	uflow-rescue	36	0
`*.f64`	`#f`	*ou**	34	0
`*.f64`	`#f`	*uo**	31	0
`acos.f64`	`(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))`	sensitivity	29	2
`pow.f64`	`#f`	sensitivity	13	0
`log.f64`	`#f`	oflow-rescue	7	0
`pow.f64`	`#f`	uflow-rescue	5	0
`log.f64`	`(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))`	uflow-rescue	1	0
↳	`(+.f64 (exp.f64 a) (exp.f64 b))`	underflow	1
↳	`(exp.f64 a)`	underflow	70
↳	`(exp.f64 b)`	underflow	52

Confusion

	Predicted +	Predicted -
+	5747	76
-	1386	6103

Precision

0.8056918547595682

Recall

0.9869483084320797

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5747	43	33
-	1386	32	6071

Precision?

0.803274139844617

Recall?

0.994332818134982

Freqs

test

number	freq
0	6179
1	4702
2	1614
3	332
4	233
5	154
6	65
7	19
8	8
9	6

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	43	0	0
-	2	1	6

Precision?

0.9347826086956522

Recall?

1.0

Samples

4.0s	7 682×	1	valid
2.8s	16 612×	0	valid
2.2s	2 070×	2	valid
558.0ms	260×	3	valid

Compiler

Compiled 19 935 to 2 551 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.7s

ival-sin: 1.1s (14.8% of total)

ival-mult: 1.0s (13.4% of total)

ival-cos: 913.0ms (11.9% of total)

adjust: 831.0ms (10.8% of total)

ival-sub: 727.0ms (9.4% of total)

ival-div: 516.0ms (6.7% of total)

ival-pow2: 394.0ms (5.1% of total)

ival-add: 353.0ms (4.6% of total)

ival-exp: 326.0ms (4.2% of total)

ival-cosu: 317.0ms (4.1% of total)

ival-sinu: 265.0ms (3.4% of total)

ival-log: 222.0ms (2.9% of total)

ival-sqrt: 171.0ms (2.2% of total)

ival-tan: 114.0ms (1.5% of total)

ival-neg: 58.0ms (0.8% of total)

ival-atan2: 55.0ms (0.7% of total)

ival-pow: 48.0ms (0.6% of total)

ival-hypot: 37.0ms (0.5% of total)

ival-atan: 33.0ms (0.4% of total)

ival-cbrt: 29.0ms (0.4% of total)

ival-true: 24.0ms (0.3% of total)

ival-acos: 21.0ms (0.3% of total)

exact: 19.0ms (0.2% of total)

ival-pi: 17.0ms (0.2% of total)

ival-assert: 13.0ms (0.2% of total)

ival-fabs: 11.0ms (0.1% of total)

ival-asin: 6.0ms (0.1% of total)

ival-log1p: 5.0ms (0.1% of total)

analyze21.0s (4.4%)

Memory

-83.0MiB live, 23 947.6MiB allocated; 9.8s collecting garbage

Algorithm

53×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	79.4%	20.6%	0%	0%	0%	0
17.2%	13.7%	65.7%	20.6%	0%	0%	0%	1
25%	19.6%	58.5%	20.6%	0%	1.3%	0%	2
35.2%	26.6%	48.9%	20.6%	0%	3.8%	0%	3
42.3%	31.7%	43.1%	20.6%	0%	4.5%	0%	4
47.9%	35.6%	38.7%	20.6%	0%	5.1%	0%	5
51%	37.6%	36.1%	20.6%	0%	5.7%	0%	6
54.4%	39.7%	33.2%	20.6%	0%	6.5%	0%	7
56.2%	40.7%	31.8%	20.6%	0%	6.8%	0%	8
59%	42.5%	29.5%	20.6%	0%	7.4%	0%	9
60.3%	43.2%	28.4%	20.6%	0%	7.7%	0%	10
62.1%	44.3%	27%	20.6%	0%	8.1%	0%	11
63.6%	45.1%	25.8%	20.6%	0%	8.5%	0%	12

Compiler

Compiled 1 826 to 963 computations (47.3% saved)

preprocess15.0s (3.2%)

Memory

683.6MiB live, 16 449.2MiB allocated; 3.9s collecting garbage

Stop Event

104×	iter limit
92×	node limit
12×	saturated

Compiler

Compiled 121 515 to 21 595 computations (82.2% saved)

bsearch14.0s (3%)

Memory

154.4MiB live, 14 452.4MiB allocated; 5.0s collecting garbage

Algorithm

328×	binary-search
83×	left-value

Stop Event

321×	narrow-enough
7×	predicate-same

Samples

5.8s	7 159×	1	valid
2.2s	13 706×	0	valid
1.0s	1 046×	2	valid
721.0ms	297×	3	valid
219.0ms	1 984×	0	invalid
49.0ms	179×	1	invalid
12.0ms	29×	2	invalid

Compiler

Compiled 262 375 to 152 749 computations (41.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0s

ival-cos: 2.2s (25.1% of total)

ival-sin: 1.5s (16.8% of total)

ival-mult: 1.3s (14.1% of total)

adjust: 797.0ms (8.9% of total)

ival-pow2: 592.0ms (6.6% of total)

ival-sub: 504.0ms (5.6% of total)

ival-div: 373.0ms (4.2% of total)

ival-sinu: 334.0ms (3.7% of total)

ival-cosu: 293.0ms (3.3% of total)

ival-add: 258.0ms (2.9% of total)

ival-sqrt: 232.0ms (2.6% of total)

ival-atan2: 221.0ms (2.5% of total)

ival-exp: 72.0ms (0.8% of total)

ival-acos: 68.0ms (0.8% of total)

ival-neg: 61.0ms (0.7% of total)

ival-tan: 23.0ms (0.3% of total)

ival-atan: 23.0ms (0.3% of total)

ival-true: 18.0ms (0.2% of total)

exact: 15.0ms (0.2% of total)

ival-log: 12.0ms (0.1% of total)

ival-asin: 10.0ms (0.1% of total)

ival-assert: 10.0ms (0.1% of total)

ival-hypot: 7.0ms (0.1% of total)

ival-pi: 7.0ms (0.1% of total)

ival-fabs: 3.0ms (0% of total)

ival-pow: 3.0ms (0% of total)

ival-log1p: 1.0ms (0% of total)

derivations13.9s (2.9%)

Memory

-284.9MiB live, 11 193.1MiB allocated; 3.0s collecting garbage

Stop Event

42×	fuel
10×	done

Compiler

Compiled 45 215 to 5 838 computations (87.1% saved)

simplify3.0s (0.6%)

Memory

115.9MiB live, 2 960.2MiB allocated; 541ms collecting garbage

Stop Event

47×	node limit
5×	saturated

start21.0ms (0%)

Memory: -21.3MiB live, 8.3MiB allocated; 25ms collecting garbage

end0.0ms (0%)

Memory: 1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

sample3.6min (46%)

rewrite53.7s (11.4%)

series33.1s (7%)

regimes30.4s (6.4%)

eval25.9s (5.5%)

prune24.0s (5.1%)

explain21.6s (4.6%)

analyze21.0s (4.4%)

preprocess15.0s (3.2%)

bsearch14.0s (3%)

derivations13.9s (2.9%)

simplify3.0s (0.6%)

start21.0ms (0%)

end0.0ms (0%)

Profiling