Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze2.0ms (0.2%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample683.0ms (61.7%)

Memory

20.3MiB live, 716.5MiB allocated; 132ms collecting garbage

Samples

463.0ms	8 256×	0	valid
0.0ms	4×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 271.0ms

ival-sqrt: 196.0ms (72.4% of total)

ival-mult!: 46.0ms (17% of total)

ival-sub!: 27.0ms (10% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

preprocess159.0ms (14.4%)

Memory

-26.3MiB live, 50.1MiB allocated; 131ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	26	19
2	52	19
3	76	19
4	135	19
5	342	19
6	2414	19
7	5901	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series6.0ms (0.5%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Counts

5 → 18

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 1))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))))
#s(approx (- 1 (* x x)) #s(hole binary64 1))
#s(approx (- 1 (* x x)) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (- 1 (* x x)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (- 1 (* x x)) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)
2.0ms	x	@	-inf	((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)
1.0ms	x	@	0	((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)

rewrite108.0ms (9.8%)

Memory

-2.1MiB live, 135.4MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	370
0	89	305
0	421	296

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

23 → 34

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 1))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))))
#s(approx (- 1 (* x x)) #s(hole binary64 1))
#s(approx (- 1 (* x x)) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (- 1 (* x x)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (- 1 (* x x)) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))))

Outputs
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(sin.f64 (acos.f64 x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(cos.f64 (asin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) (.f64 #s(literal 1 binary64) (*.f64 x x)))))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
#s(literal 1 binary64)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- 1 (* x x)) #s(literal 1 binary64))
#s(approx (- 1 (* x x)) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (- 1 (* x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x))
#s(approx (- 1 (* x x)) (neg.f64 (*.f64 x x)))
#s(approx (- 1 (* x x)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x)))

eval5.0ms (0.4%)

Memory: 6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 270 to 123 computations (54.4% saved)

prune2.0ms (0.2%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	3	30

Accuracy

100.0%

Counts

30 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	98.7%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Status

Accuracy

Program

✓

100.0%

(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

▶

99.6%

#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))

▶

98.7%

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 22 to 22 computations (0% saved)

series2.0ms (0.2%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Counts

7 → 18

Calls

Call 1

Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 1))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)
1.0ms	x	@	-inf	((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)
0.0ms	x	@	0	((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)

Time

Variable

Point

Expression

1.0ms

inf

((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)

1.0ms

-inf

((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)

0.0ms

((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2)

rewrite98.0ms (8.9%)

Memory

-17.0MiB live, 42.5MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	391
0	88	323
0	422	315

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

25 → 39

Calls

Call 1

Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 1))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))))
#s(approx (sqrt (- 1 (* x x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))))

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(literal -1/2 binary64)
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64))
#s(approx (+ (* (* x x) -1/2) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (- 1 (* x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) x)))

eval3.0ms (0.2%)

Memory: 5.5MiB live, 5.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 308 to 137 computations (55.5% saved)

prune2.0ms (0.2%)

Memory

2.6MiB live, 2.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	30	3	33

Accuracy

100.0%

Counts

33 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	98.7%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Status

Accuracy

Program

✓

100.0%

(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

✓

99.6%

#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))

✓

98.7%

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 39 to 35 computations (10.3% saved)

regimes5.0ms (0.4%)

Memory

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))

Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
100.0%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes3.0ms (0.3%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
98.7%	1	`(*.f64 x x)`
98.7%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
98.7%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
98.7%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

derivations2.0ms (0.2%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 10 computations (0% saved)

preprocess25.0ms (2.3%)

Memory: -15.9MiB live, 32.3MiB allocated; 4ms collecting garbage
Remove: (abs x)
Compiler: Compiled 39 to 39 computations (0% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze2.0ms (0.2%)

sample683.0ms (61.7%)

preprocess159.0ms (14.4%)

series6.0ms (0.5%)

rewrite108.0ms (9.8%)

eval5.0ms (0.4%)

prune2.0ms (0.2%)

series2.0ms (0.2%)

rewrite98.0ms (8.9%)

eval3.0ms (0.2%)

prune2.0ms (0.2%)

regimes5.0ms (0.4%)

regimes3.0ms (0.3%)

derivations2.0ms (0.2%)

preprocess25.0ms (2.3%)

end0.0ms (0%)

Profiling