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

2.0MiB live, 2.0MiB 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)

sample827.0ms (81%)

Memory

96.4MiB live, 977.6MiB allocated; 329ms collecting garbage

Samples

645.0ms	8 256×	0	valid
0.0ms	6×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 205.0ms

ival-sqrt: 109.0ms (53.2% of total)

ival-mult!: 62.0ms (30.2% of total)

ival-sub!: 33.0ms (16.1% of total)

adjust: 1.0ms (0.5% of total)

Bogosity

preprocess32.0ms (3.1%)

Memory

-14.4MiB live, 30.6MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	10
1	47	10
2	151	10
3	1026	10

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)

series3.0ms (0.3%)

Memory

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

Counts

5 → 17

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 (* -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
1.0ms	x	@	inf	((sqrt (- 1 (* x x))) (- 1 (* x x)) 1 (* x x) x)
1.0ms	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)

rewrite39.0ms (3.8%)

Memory

10.4MiB live, 55.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	363
0	88	297
0	523	285

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

22 → 45

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 (* -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))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (neg.f64 (.f64 x x)))) (-.f64 #s(literal 1 binary64) (neg.f64 (.f64 x 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 (neg.f64 (.f64 x x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (neg.f64 (.f64 x x)) (neg.f64 (.f64 x x))) (.f64 #s(literal 1 binary64) (neg.f64 (.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)))))
(neg.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x x))))
(-.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x)))
#s(literal 1 binary64)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.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 (fma.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 (fma.f64 (fma.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)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
#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)))

eval4.0ms (0.4%)

Memory: 7.4MiB live, 7.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 331 to 155 computations (53.2% saved)

prune2.0ms (0.2%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Accuracy

100.0%

Counts

41 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	99.1%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	98.2%	#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)))

▶

99.1%

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

▶

98.2%

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

Compiler

Compiled 22 to 22 computations (0% saved)

series2.0ms (0.2%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Counts

7 → 16

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) #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)

rewrite59.0ms (5.8%)

Memory

-5.4MiB live, 39.4MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	369
0	86	302
0	523	291

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

23 → 41

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) #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)) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) (.f64 (*.f64 x x) #s(literal -1/2 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 (.f64 (.f64 x 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 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64))))
(+.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 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.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 (fma.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 (fma.f64 (fma.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) (*.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 (0.3%)

Memory: 7.6MiB live, 7.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 316 to 142 computations (55.1% saved)

prune2.0ms (0.2%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	32	3	35

Accuracy

100.0%

Counts

35 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.1%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	98.2%	#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)))

✓

99.1%

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

✓

98.2%

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

Compiler

Compiled 39 to 35 computations (10.3% saved)

regimes23.0ms (2.3%)

Memory

-23.3MiB live, 23.9MiB allocated; 17ms 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:

19.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (-.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

10.5MiB live, 10.5MiB 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
98.2%	1	`(*.f64 x x)`
98.2%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
98.2%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
98.2%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

derivations2.0ms (0.2%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 10 computations (0% saved)

preprocess17.0ms (1.7%)

Memory: -9.7MiB live, 34.5MiB allocated; 7ms 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%)

sample827.0ms (81%)

preprocess32.0ms (3.1%)

series3.0ms (0.3%)

rewrite39.0ms (3.8%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

series2.0ms (0.2%)

rewrite59.0ms (5.8%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

regimes23.0ms (2.3%)

regimes3.0ms (0.3%)

derivations2.0ms (0.2%)

preprocess17.0ms (1.7%)

end0.0ms (0%)

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