Metrics for Herbie run

Date:	Sunday, January 19th, 2025
Commit:	7183cd93 on autofix-12-1
Seed:	2025019
Parameters:	256 points for 4 iterations
Flags:	`localize:costslocalize:errorsreduce:regimesreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default
Memory:	636 006.5 MB

sample3.9min (39%)

Memory

1 596.6MiB live, 232 747.9MiB allocated; 1.1min collecting garbage

Samples

56.7s	119 720×	1	valid
55.4s	17 997×	5	exit
41.8s	281 749×	0	valid
17.5s	24 659×	2	valid
7.4s	3 162×	3	valid
6.8s	35 339×	0	exit
4.5s	19 750×	0	invalid
3.0s	12 050×	1	invalid
464.0ms	871×	2	invalid
173.0ms	22×	4	valid
25.0ms	48×	1	exit
2.0ms	2×	2	exit

Precisions

Click to see histograms. Total time spent on operations: 2.8min

ival-pow: 46.8s (27.6% of total)

ival-mult: 18.6s (10.9% of total)

adjust: 15.9s (9.4% of total)

ival-cos: 11.2s (6.6% of total)

ival-div: 11.0s (6.5% of total)

ival-sin: 10.0s (5.9% of total)

ival-pow2: 7.7s (4.5% of total)

ival-add: 6.8s (4% of total)

ival-sub: 6.7s (4% of total)

ival-exp: 6.1s (3.6% of total)

ival-sinu: 5.3s (3.1% of total)

ival-cosu: 4.5s (2.7% of total)

ival-log: 4.5s (2.6% of total)

ival-sqrt: 3.6s (2.1% of total)

ival-neg: 1.9s (1.1% of total)

ival-<: 1.8s (1.1% of total)

const: 1.6s (0.9% of total)

ival-log1p: 999.0ms (0.6% of total)

ival-atan2: 772.0ms (0.5% of total)

ival-tan: 718.0ms (0.4% of total)

ival-hypot: 646.0ms (0.4% of total)

exact: 380.0ms (0.2% of total)

ival-acos: 347.0ms (0.2% of total)

ival-and: 346.0ms (0.2% of total)

ival-atan: 322.0ms (0.2% of total)

ival-true: 289.0ms (0.2% of total)

ival-cbrt: 282.0ms (0.2% of total)

ival-assert: 212.0ms (0.1% of total)

ival-fabs: 170.0ms (0.1% of total)

ival-<=: 121.0ms (0.1% of total)

ival-pi: 112.0ms (0.1% of total)

ival-asin: 105.0ms (0.1% of total)

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

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

Bogosity

simplify1.3min (13.4%)

Memory

670.2MiB live, 80 608.9MiB allocated; 16.8s collecting garbage

Stop Event

609×	iter limit
431×	node limit
19×	saturated
2×	unsound

Counts

30 268 → 30 268

localize1.2min (12%)

Memory

689.9MiB live, 78 355.0MiB allocated; 17.9s collecting garbage

Samples

27.2s	16 235×	1	valid
10.3s	4 168×	2	valid
9.8s	27 526×	0	valid
7.2s	709×	5	exit
1.1s	1 978×	0	invalid
898.0ms	371×	3	valid
333.0ms	128×	1	invalid
117.0ms	11×	4	exit
23.0ms	71×	0	exit
4.0ms	3×	4	valid

Compiler

Compiled 118 306 to 9 300 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.8s

ival-mult: 9.0s (19.2% of total)

ival-sin: 7.7s (16.5% of total)

adjust: 5.9s (12.7% of total)

ival-cos: 5.1s (11% of total)

ival-div: 4.1s (8.7% of total)

ival-add: 2.8s (5.9% of total)

ival-pow2: 2.1s (4.4% of total)

const: 1.4s (2.9% of total)

ival-sub: 1.3s (2.8% of total)

ival-pow: 1.2s (2.6% of total)

ival-sinu: 1.2s (2.6% of total)

ival-sqrt: 895.0ms (1.9% of total)

ival-log: 719.0ms (1.5% of total)

ival-exp: 654.0ms (1.4% of total)

ival-cosu: 653.0ms (1.4% of total)

ival-neg: 455.0ms (1% of total)

ival-atan2: 275.0ms (0.6% of total)

ival-hypot: 217.0ms (0.5% of total)

ival-cbrt: 165.0ms (0.4% of total)

ival-tan: 156.0ms (0.3% of total)

ival-acos: 137.0ms (0.3% of total)

exact: 102.0ms (0.2% of total)

ival-atan: 97.0ms (0.2% of total)

ival-pi: 80.0ms (0.2% of total)

ival-asin: 65.0ms (0.1% of total)

ival-fabs: 61.0ms (0.1% of total)

ival-cosh: 52.0ms (0.1% of total)

ival-asinh: 45.0ms (0.1% of total)

ival-true: 44.0ms (0.1% of total)

ival-log1p: 31.0ms (0.1% of total)

ival-assert: 23.0ms (0% of total)

ival-expm1: 13.0ms (0% of total)

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

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

ival-sinh: 5.0ms (0% of total)

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

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

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

regimes37.3s (6.3%)

Memory

-223.3MiB live, 43 971.4MiB allocated; 9.5s collecting garbage

Counts

19 214 → 862

Calls

155 calls:

3.3s	phi1
2.3s	phi2
2.3s	lambda2
1.9s	lambda1
1.7s	(atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) #s(literal 2 binary64)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) #s(literal 2 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) #s(literal 2 binary64)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) #s(literal 2 binary64))))))))

Compiler

Compiled 20 127 to 15 794 computations (21.5% saved)

series28.5s (4.8%)

Memory

-571.1MiB live, 32 381.9MiB allocated; 10.3s collecting garbage

Counts

3 669 → 30 268

Calls

1638 calls:

Time	Variable		Point	Expression
1.1s	c_n	@	-inf	((/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (/ (pow (- 1 (/ 1 (+ (exp (neg s)) 1))) c_n) (pow (- 1 (/ 1 (+ (exp (neg t)) 1))) c_n)) (pow (- 1 (/ 1 (+ (exp (neg s)) 1))) c_n) (- 1 (/ 1 (+ (exp (neg s)) 1))) (/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (/ (pow (/ 1 (+ (exp (neg s)) 1)) c_p) (pow (/ 1 (+ (exp (neg t)) 1)) c_p)) (pow (/ 1 (+ (exp (neg s)) 1)) c_p) (/ 1 (+ (exp (neg s)) 1)) (/ (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (* (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (pow (/ 1 (+ 1 (exp (neg s)))) c_p) (/ 1 (+ 1 (exp (neg s)))) (* -1 c_p) (/ (* (pow (- (exp (neg s)) -1) (* -1 c_p)) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (* (pow (- (exp (neg s)) -1) (* -1 c_p)) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (pow (- (exp (neg s)) -1) (* -1 c_p)) (/ (* (pow (pow (- (exp (neg s)) -1) -2) (/ c_p 2)) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (neg t))))) c_n))) (* (pow (pow (- (exp (neg s)) -1) -2) (/ c_p 2)) (pow (- 1 (/ 1 (+ 1 (exp (neg s))))) c_n)) (pow (pow (- (exp (neg s)) -1) -2) (/ c_p 2)) (pow (- (exp (neg s)) -1) -2) (- 1 (/ 1 (+ (exp (neg t)) 1))) (pow (/ 1 (+ (exp (neg t)) 1)) c_p) (pow (/ 1 (+ 1 (exp (neg t)))) c_p) (- 1 (/ 1 (+ 1 (exp (neg s))))) (pow (/ 1 (+ 1 (exp (neg t)))) c_p))
924.0ms	lambda1	@	0	((* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))) (sqrt (+ (* (* (cos (* -1/2 phi2)) (- lambda1 lambda2)) (* (cos (* -1/2 phi2)) (- lambda1 lambda2))) (* phi2 phi2))) (* (cos (* -1/2 phi2)) (- lambda1 lambda2)) (+ (* -1 phi1) phi2) (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (* (neg phi1) (+ (* (neg R) (/ phi2 phi1)) R)) (* (+ (* -1 phi1) phi2) R) (/ (* phi1 R) phi1) (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (* (neg phi1) (+ (* (neg R) (/ phi2 phi1)) R)) (neg phi1) (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (* (* R lambda1) (cos (* 1/2 (+ phi2 phi1)))) (* R lambda1) (cos (* 1/2 (+ phi2 phi1))) (* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))) (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))) (sqrt (+ (* (* (cos (* -1/2 phi2)) (- lambda1 lambda2)) (* (cos (* -1/2 phi2)) (- lambda1 lambda2))) (* phi2 phi2))) (* (cos (* -1/2 phi2)) (- lambda1 lambda2)) (+ (* phi2 (/ (neg R) phi1)) (/ (* phi1 R) phi1)) (* 1/2 (+ phi2 phi1)) (* (cos (* 1/2 phi2)) lambda1))
526.0ms	x	@	inf	((+ (* (tan x) (neg (tan x))) 1) (* (tan x) (tan x)) (/ (+ (* (tan x) (neg (tan x))) 1) (+ 1 (* (tan x) (tan x)))) (tan x) (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (/ (- 1 (pow (tan x) 2)) (+ 1 (* (tan x) (tan x)))) (- 1 (pow (tan x) 2)) (pow (tan x) 2) (/ (- 1 (pow (tan x) 4)) (* (+ (* (tan x) (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (- 1 (pow (tan x) 4)) (pow (tan x) 4) (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1)) (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ 1 (* (tan x) (tan x))) (* (+ (* (tan x) (tan x)) 1) (+ (* (tan x) (tan x)) 1)) (+ (* (tan x) (tan x)) 1) (pow (sin x) 2) (pow (cos x) 2) (/ (sin x) (pow (cos x) 2)))
475.0ms	a	@	inf	((/ (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 (sqrt 2)) (sqrt 8))) (* 1/4 a) (* (* x-scale (sqrt 2)) (sqrt 8)) (* 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))))))) (/ (* 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)))))) (/ (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 (* (* (* (sqrt 8) y-scale) x-scale) b)) (sqrt (- (+ (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale)) (/ (pow (cos (* -1/180 (* (PI) angle))) 2) (* x-scale x-scale))) (sqrt (+ (* (* (pow (cos (* -1/180 (* (PI) angle))) 2) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (pow (* y-scale x-scale) 2))) 4) (pow (- (/ (pow (cos (* -1/180 (* (PI) angle))) 2) (* x-scale x-scale)) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale))) 2)))))) (* 1/4 (* (* (* (sqrt 8) y-scale) x-scale) b)) (* (* (* (sqrt 8) y-scale) x-scale) b) (+ (* (/ (pow (cos (* -1/180 (* (PI) angle))) 2) x-scale) (/ (* b b) x-scale)) (* (/ (* b b) y-scale) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) y-scale))) (+ (* (/ (pow (cos (* -1/180 (* (PI) angle))) 2) x-scale) (/ (* b b) x-scale)) (* (* (neg b) b) (/ (pow (sin (* (* (PI) angle) 1/180)) 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))) (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* -1/180 (* (PI) angle))) 2)) y-scale)) (* (* -2 (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* a a)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* b b)))) (/ (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* b b)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* a a))) (* y-scale y-scale)))) (- (/ (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* b b)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* a a))) (* y-scale y-scale)) (* (/ (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* -1/180 (* (PI) angle))) 2)) y-scale)) (* (* -2 (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* a a)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* b b)))) (/ (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* b b)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* a a))) (* y-scale y-scale)))) (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* a a)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* b b)))) 1/2)) (/ (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))))))) (/ (* 4 (* (* b a) (* b (neg a)))) (pow (* x-scale y-scale) 2))) (* (* 1/4 (* (* (sqrt 8) y-scale) x-scale)) (sqrt (- (/ (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* b b)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* a a))) (* y-scale y-scale)) (* (/ (+ (* (/ 4 y-scale) (/ (* (* (pow (* (+ b a) (- b a)) 2) (pow (sin (* (* (PI) angle) 1/180)) 2)) (pow (cos (* -1/180 (* (PI) angle))) 2)) y-scale)) (* (* -2 (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* a a)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* b b)))) (/ (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* b b)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* a a))) (* y-scale y-scale)))) (+ (* (pow (sin (* (* (PI) angle) 1/180)) 2) (* a a)) (* (pow (cos (* -1/180 (* (PI) angle))) 2) (* b b)))) 1/2)))) (sqrt 2) (sqrt 8) (- (+ (/ (/ (+ (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)))) (neg a) (PI) (cos (* -1/180 (* (PI) angle))) (sin (* (* (PI) angle) 1/180)) (- (+ (/ (/ (+ (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)))))
331.0ms	a	@	inf	((* 180 (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI))) (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI)) (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale)) (* (* (/ x-scale angle) (/ (* (* 2 (- (/ (* a a) (* y-scale y-scale)) (/ (* b b) (* x-scale x-scale)))) y-scale) (* (* (+ b a) (- b a)) (PI)))) 90) (* 180 (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI))) (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI)) (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (* 180 (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI))) (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI)) (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale)) (* 180 (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI))) (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI)) (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-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))) (* 180 (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI))) (/ (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (PI)) (atan (/ (- (- (/ (/ (+ (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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))) (cos (* -1/180 (* (PI) angle))) (sin (* (* (PI) angle) 1/180)) (* (* x-scale y-scale) (- (- (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale)) (sqrt (+ (* (* (pow (cos (* -1/180 (* (PI) angle))) 2) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* (* y-scale x-scale) (* y-scale x-scale)))) 4) (pow (- (/ (pow (cos (* -1/180 (* (PI) angle))) 2) (* x-scale x-scale)) (/ (pow (sin (* (* (PI) angle) 1/180)) 2) (* y-scale y-scale))) 2)))) (/ (pow (cos (* -1/180 (* (PI) angle))) 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)) (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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale)) (/ (* (* 2 (- (/ (* a a) (* y-scale y-scale)) (/ (* b b) (* x-scale x-scale)))) y-scale) (* (* (+ b a) (- b a)) (PI))) (/ (* b b) (* x-scale x-scale)) (/ (* a a) (* 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))) (cos (* (/ angle 180) (PI))) (sin (* (/ 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 (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-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 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale)))

rewrite22.8s (3.8%)

Memory

297.7MiB live, 23 352.9MiB allocated; 3.9s collecting garbage

Stop Event

604×	iter limit
154×	node limit
41×	unsound
5×	saturated

Counts

3 669 → 51 492

explain20.8s (3.5%)

Memory

-176.8MiB live, 25 225.2MiB allocated; 3.1s collecting garbage

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`#f`	sensitivity	1951	2
`sin.f64`	`#f`	sensitivity	1687	2
`+.f64`	`#f`	cancellation	1682	39
`sqrt.f64`	`#f`	oflow-rescue	1389	0
`-.f64`	`#f`	cancellation	907	9
`-.f64`	`#f`	nan-rescue	591	0
`log.f64`	`#f`	sensitivity	577	1
`/.f64`	`#f`	o/n	486	0
`/.f64`	`#f`	o/o	356	0
`/.f64`	`#f`	u/u	291	0
`*.f64`	`#f`	*no**	248	0
`sqrt.f64`	`#f`	uflow-rescue	155	0
`exp.f64`	`#f`	sensitivity	155	23
`/.f64`	`#f`	u/n	141	0
`/.f64`	`#f`	n/o	102	0
`cbrt.f64`	`#f`	oflow-rescue	94	0
`*.f64`	`#f`	*nu**	75	0
`*.f64`	`#f`	*ou**	39	0
`/.f64`	`#f`	n/u	38	0
`cbrt.f64`	`#f`	uflow-rescue	38	0
`*.f64`	`#f`	*uo**	24	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	15	4
`log.f64`	`#f`	oflow-rescue	7	0
`pow.f64`	`#f`	uflow-rescue	6	0
`pow.f64`	`#f`	sensitivity	5	2
`asin.f64`	`(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))`	sensitivity	1	2

Confusion

	Predicted +	Predicted -
+	5671	76
-	1361	6204

Precision

0.8064562002275313

Recall

0.9867757090655994

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5671	48	28
-	1361	29	6175

Precision?

0.8044732029821353

Recall?

0.9951278928136419

Freqs

test

number	freq
0	6280
1	4608
2	1622
3	341
4	238
5	146
6	46
7	23
8	6
9	2

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	43	0	0
-	2	0	7

Precision?

0.9555555555555556

Recall?

1.0

Samples

3.8s	7 554×	1	valid
2.4s	16 724×	0	valid
2.3s	2 052×	2	valid
584.0ms	294×	3	valid

Compiler

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

Precisions

Click to see histograms. Total time spent on operations: 7.4s

ival-sin: 1.2s (16.5% of total)

ival-mult: 1.0s (13.9% of total)

ival-cos: 881.0ms (11.8% of total)

adjust: 844.0ms (11.4% of total)

ival-div: 521.0ms (7% of total)

ival-pow2: 441.0ms (5.9% of total)

ival-cosu: 322.0ms (4.3% of total)

ival-add: 300.0ms (4% of total)

ival-sinu: 296.0ms (4% of total)

ival-sub: 294.0ms (4% of total)

ival-exp: 280.0ms (3.8% of total)

ival-log: 242.0ms (3.3% of total)

ival-sqrt: 202.0ms (2.7% of total)

ival-hypot: 156.0ms (2.1% of total)

ival-neg: 64.0ms (0.9% of total)

ival-atan: 57.0ms (0.8% of total)

ival-tan: 45.0ms (0.6% of total)

ival-acos: 41.0ms (0.6% of total)

ival-atan2: 40.0ms (0.5% of total)

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

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

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

exact: 19.0ms (0.3% of total)

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

ival-asin: 15.0ms (0.2% of total)

ival-assert: 12.0ms (0.2% of total)

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

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

derivations20.3s (3.4%)

Memory

-183.0MiB live, 14 861.0MiB allocated; 3.0s collecting garbage

Stop Event

45×	fuel
7×	done

Compiler

Compiled 44 619 to 5 781 computations (87% saved)

analyze19.4s (3.3%)

Memory

256.1MiB live, 20 789.8MiB allocated; 5.8s 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)

prune18.9s (3.2%)

Memory: 64.9MiB live, 29 451.3MiB allocated; 3.3s collecting garbage
Counts: 87 766 → 6 518
Compiler: Compiled 1 049 213 to 397 350 computations (62.1% saved)

eval18.5s (3.1%)

Memory: 445.3MiB live, 23 721.8MiB allocated; 6.0s collecting garbage
Compiler: Compiled 7 956 881 to 437 235 computations (94.5% saved)

preprocess13.7s (2.3%)

Memory

650.4MiB live, 15 237.0MiB allocated; 2.1s collecting garbage

Stop Event

104×	iter limit
92×	node limit
12×	saturated

Compiler

Compiled 121 297 to 21 581 computations (82.2% saved)

bsearch11.2s (1.9%)

Memory

337.9MiB live, 15 294.8MiB allocated; 1.8s collecting garbage

Algorithm

297×	binary-search
84×	left-value

Stop Event

290×	narrow-enough
7×	predicate-same

Samples

4.9s	6 753×	1	valid
2.7s	13 490×	0	valid
680.0ms	763×	2	valid
436.0ms	162×	3	valid
87.0ms	586×	0	invalid

Compiler

Compiled 252 936 to 151 087 computations (40.3% saved)

Precisions

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

ival-sin: 1.7s (21.9% of total)

ival-cos: 1.6s (20.8% of total)

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

adjust: 635.0ms (8.2% of total)

ival-pow2: 442.0ms (5.7% of total)

ival-div: 407.0ms (5.3% of total)

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

ival-cosu: 319.0ms (4.1% of total)

ival-sinu: 284.0ms (3.7% of total)

ival-add: 168.0ms (2.2% of total)

ival-acos: 148.0ms (1.9% of total)

ival-sqrt: 138.0ms (1.8% of total)

ival-atan2: 120.0ms (1.5% of total)

ival-neg: 110.0ms (1.4% of total)

ival-tan: 89.0ms (1.1% of total)

ival-exp: 69.0ms (0.9% of total)

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

ival-atan: 31.0ms (0.4% of total)

ival-log: 16.0ms (0.2% of total)

ival-true: 16.0ms (0.2% of total)

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

exact: 10.0ms (0.1% of total)

ival-assert: 9.0ms (0.1% of total)

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

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

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

start3.0ms (0%)

Memory: 6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

end0.0ms (0%)

Memory: 0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

sample3.9min (39%)

simplify1.3min (13.4%)

localize1.2min (12%)

regimes37.3s (6.3%)

series28.5s (4.8%)

rewrite22.8s (3.8%)

explain20.8s (3.5%)

derivations20.3s (3.4%)

analyze19.4s (3.3%)

prune18.9s (3.2%)

eval18.5s (3.1%)

preprocess13.7s (2.3%)

bsearch11.2s (1.9%)

start3.0ms (0%)

end0.0ms (0%)

Profiling