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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze2.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB 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)

sample855.0ms (49.3%)

Memory

19.1MiB live, 761.7MiB allocated; 231ms collecting garbage

Samples

569.0ms	8 256×	0	valid
0.0ms	2×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 347.0ms

ival-mult: 189.0ms (54.5% of total)

ival-sub: 97.0ms (28% of total)

ival-sqrt: 51.0ms (14.7% of total)

exact: 5.0ms (1.4% of total)

adjust: 2.0ms (0.6% of total)

ival-assert: 2.0ms (0.6% of total)

Bogosity

explain59.0ms (3.4%)

Memory

6.9MiB live, 105.3MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

23.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (38.3% of total)

ival-sqrt: 4.0ms (38.3% of total)

ival-sub: 2.0ms (19.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess247.0ms (14.2%)

Memory

-9.7MiB live, 230.8MiB allocated; 64ms 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
0	5	6
0	8	6
1	16	6
2	40	6
3	79	6
4	138	6
5	345	6
6	2407	6
7	5971	6
0	8210	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

series3.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB 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
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)

rewrite49.0ms (2.8%)

Memory

22.3MiB live, 68.0MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	370
0	90	305
0	422	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) (pow.f64 x #s(literal 4 binary64))) (+.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) (+.f64 (pow.f64 x #s(literal 4 binary64)) (.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)) (fma.f64 #s(literal -1 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 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
#s(approx (sqrt (- 1 (* x x))) (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (sqrt (- 1 (* x x))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (- 1 (* x x)) (neg.f64 (*.f64 x x)))
#s(approx (- 1 (* x x)) (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #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 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))
#s(approx (sqrt (- 1 (* x x))) (neg.f64 (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))

eval8.0ms (0.5%)

Memory: -27.1MiB live, 19.3MiB allocated; 4ms collecting garbage
Compiler: Compiled 467 to 128 computations (72.6% saved)

prune2.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Accuracy

100.0%

Counts

37 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	99.4%	#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 31 computations (20.5% saved)

series5.0ms (0.3%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Counts

13 → 43

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)
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 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 (+ (* (* 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 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 1))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (- 1 (pow x 4)) #s(hole binary64 1))
#s(approx (- 1 (pow x 4)) #s(hole binary64 (+ 1 (* -1 (pow x 4)))))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (+ 1 (* x x)) #s(hole binary64 1))
#s(approx (+ 1 (* x x)) #s(hole binary64 (+ 1 (pow x 2))))
#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 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (- 1 (pow x 4)) #s(hole binary64 (* -1 (pow x 4))))
#s(approx (- 1 (pow x 4)) #s(hole binary64 (* (pow x 4) (- (/ 1 (pow x 4)) 1))))
#s(approx (+ 1 (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ 1 (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 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)))))))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 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 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (/ (- 1 (pow x 4)) (+ 1 (* x x))) (- 1 (pow x 4)) (pow x 4) 4 (+ 1 (* x x)))
1.0ms	x	@	-inf	((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (/ (- 1 (pow x 4)) (+ 1 (* x x))) (- 1 (pow x 4)) (pow x 4) 4 (+ 1 (* x x)))
1.0ms	x	@	0	((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (/ (- 1 (pow x 4)) (+ 1 (* x x))) (- 1 (pow x 4)) (pow x 4) 4 (+ 1 (* x x)))

Time

Variable

Point

Expression

2.0ms

inf

((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (/ (- 1 (pow x 4)) (+ 1 (* x x))) (- 1 (pow x 4)) (pow x 4) 4 (+ 1 (* x x)))

1.0ms

-inf

((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (/ (- 1 (pow x 4)) (+ 1 (* x x))) (- 1 (pow x 4)) (pow x 4) 4 (+ 1 (* x x)))

1.0ms

((sqrt (- 1 (* x x))) 1 (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) x -1/2 (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (/ (- 1 (pow x 4)) (+ 1 (* x x))) (- 1 (pow x 4)) (pow x 4) 4 (+ 1 (* x x)))

rewrite62.0ms (3.6%)

Memory

-23.7MiB live, 77.6MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	967
0	144	719
0	580	697

Stop Event

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

Counts

56 → 91

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)
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
(+.f64 #s(literal 1 binary64) (*.f64 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 (+ (* (* 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 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 1))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (- 1 (pow x 4)) #s(hole binary64 1))
#s(approx (- 1 (pow x 4)) #s(hole binary64 (+ 1 (* -1 (pow x 4)))))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (+ 1 (* x x)) #s(hole binary64 1))
#s(approx (+ 1 (* x x)) #s(hole binary64 (+ 1 (pow x 2))))
#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 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (- 1 (pow x 4)) #s(hole binary64 (* -1 (pow x 4))))
#s(approx (- 1 (pow x 4)) #s(hole binary64 (* (pow x 4) (- (/ 1 (pow x 4)) 1))))
#s(approx (+ 1 (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ 1 (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 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)))))))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x)))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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)
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 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) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(.f64 (.f64 x x) (*.f64 x x))
(pow.f64 x #s(literal 4 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
#s(literal 4 binary64)
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) #s(literal 1 binary64))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x)))) #s(literal 1 binary64))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 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 (pow x 4)) (+ 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 (pow x 4)) (+ 1 (* x x))) #s(literal 1 binary64))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) (fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- 1 (pow x 4)) #s(literal 1 binary64))
#s(approx (- 1 (pow x 4)) (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
#s(approx (pow x 4) (pow.f64 x #s(literal 4 binary64)))
#s(approx (+ 1 (* x x)) #s(literal 1 binary64))
#s(approx (+ 1 (* x x)) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) (neg.f64 (*.f64 x x)))
#s(approx (/ (- 1 (pow x 4)) (+ 1 (* x x))) (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (- 1 (pow x 4)) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
#s(approx (- 1 (pow x 4)) (*.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1 (* x x)) (*.f64 x x))
#s(approx (+ 1 (* x x)) (.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))
#s(approx (sqrt (/ (- 1 (pow x 4)) (+ 1 (* x x)))) (neg.f64 (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))

eval9.0ms (0.5%)

Memory: 21.9MiB live, 21.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 608 to 309 computations (80.8% saved)

prune4.0ms (0.2%)

Memory

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

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	95	4	99

Accuracy

100.0%

Counts

99 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.4%	#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 43 to 30 computations (30.2% saved)

series5.0ms (0.3%)

Memory

-38.5MiB live, 8.0MiB allocated; 2ms collecting garbage

Counts

8 → 27

Calls

Call 1

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

Outputs
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 1 (* x x))) #s(hole binary64 1))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 1))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 4)))))
#s(approx (* (* x x) (* x x)) #s(hole binary64 (pow x 4)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ 1 (* x x)) #s(hole binary64 1))
#s(approx (+ 1 (* x x)) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 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) (* x x))) (+ 1 (* x x))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (* -1 (pow x 4))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (* (pow x 4) (- (/ 1 (pow x 4)) 1))))
#s(approx (+ 1 (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ 1 (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 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
3.0ms	x	@	inf	((sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) (- 1 (* (* x x) (* x x))) 1 (* (* x x) (* x x)) (* x x) x (+ 1 (* x x)))
1.0ms	x	@	-inf	((sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) (- 1 (* (* x x) (* x x))) 1 (* (* x x) (* x x)) (* x x) x (+ 1 (* x x)))
1.0ms	x	@	0	((sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) (- 1 (* (* x x) (* x x))) 1 (* (* x x) (* x x)) (* x x) x (+ 1 (* x x)))

Time

Variable

Point

Expression

3.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

rewrite84.0ms (4.8%)

Memory

27.3MiB live, 72.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	690
0	120	558
0	537	525

Stop Event

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

Counts

35 → 62

Calls

Call 1

Inputs
(sqrt.f64 (/.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) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))
#s(literal 1 binary64)
(.f64 (.f64 x x) (*.f64 x x))
(*.f64 x x)
x
(+.f64 #s(literal 1 binary64) (*.f64 x x))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 1 (* x x))) #s(hole binary64 1))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 1))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 4)))))
#s(approx (* (* x x) (* x x)) #s(hole binary64 (pow x 4)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ 1 (* x x)) #s(hole binary64 1))
#s(approx (+ 1 (* x x)) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 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) (* x x))) (+ 1 (* x x))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (* -1 (pow x 4))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (* (pow x 4) (- (/ 1 (pow x 4)) 1))))
#s(approx (+ 1 (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (+ 1 (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 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 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (*.f64 x x)))
#s(literal 1 binary64)
(.f64 (.f64 (*.f64 x x) x) x)
(.f64 (fabs.f64 (.f64 x x)) (fabs.f64 (*.f64 x x)))
(.f64 (neg.f64 (.f64 x x)) (neg.f64 (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 x (.f64 x (*.f64 x x)))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 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
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) #s(literal 1 binary64))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 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) (* x x))) (+ 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) (* x x))) (+ 1 (* x x))) #s(literal 1 binary64))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) (fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- 1 (* (* x x) (* x x))) #s(literal 1 binary64))
#s(approx (- 1 (* (* x x) (* x x))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) #s(literal 1 binary64)))
#s(approx (* (* x x) (* x x)) (pow.f64 x #s(literal 4 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ 1 (* x x)) #s(literal 1 binary64))
#s(approx (+ 1 (* x x)) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) (neg.f64 (*.f64 x x)))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x))) (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (- 1 (* (* x x) (* x x))) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
#s(approx (- 1 (* (* x x) (* x x))) (*.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1 (* x x)) (*.f64 x x))
#s(approx (+ 1 (* x x)) (.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (neg.f64 (*.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (neg.f64 (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ 1 (* x x)))) (neg.f64 (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (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 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x)))

eval42.0ms (2.4%)

Memory: -6.3MiB live, 35.5MiB allocated; 17ms collecting garbage
Compiler: Compiled 1 728 to 317 computations (81.7% saved)

prune3.0ms (0.2%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	87	4	91

Accuracy

100.0%

Counts

91 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.4%	#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 42 to 30 computations (28.6% saved)

series4.0ms (0.2%)

Memory

13.2MiB live, 13.2MiB allocated; 0ms collecting garbage

Counts

8 → 27

Calls

Call 1

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

Outputs
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1)) #s(hole binary64 1))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1)) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 1))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (+ 1 (* -1 (pow x 4)))))
#s(approx (* (* x x) (* x x)) #s(hole binary64 (pow x 4)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (* x (sqrt -1))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #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) (* x x))) (+ (* x x) 1))) #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) (* x x))) (+ (* x x) 1)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1)) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (* -1 (pow x 4))))
#s(approx (- 1 (* (* x x) (* x x))) #s(hole binary64 (* (pow x 4) (- (/ 1 (pow x 4)) 1))))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (* -1 (* x (sqrt -1)))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #s(hole binary64 (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))))
#s(approx (sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) #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) (* x x))) (+ (* x x) 1))) #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) (* x x))) (+ (* x x) 1))) (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1)) (- 1 (* (* x x) (* x x))) 1 (* (* x x) (* x x)) (* x x) x (+ (* x x) 1))
1.0ms	x	@	-inf	((sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1)) (- 1 (* (* x x) (* x x))) 1 (* (* x x) (* x x)) (* x x) x (+ (* x x) 1))
1.0ms	x	@	0	((sqrt (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1))) (/ (- 1 (* (* x x) (* x x))) (+ (* x x) 1)) (- 1 (* (* x x) (* x x))) 1 (* (* x x) (* x x)) (* x x) x (+ (* x x) 1))

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

rewrite104.0ms (6%)

Memory

8.8MiB live, 126.5MiB allocated; 78ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	667
0	118	534
0	540	525

Stop Event

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

Counts

35 → 63

Calls

Call 1

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

eval8.0ms (0.5%)

Memory: 21.4MiB live, 21.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 592 to 305 computations (80.8% saved)

prune38.0ms (2.2%)

Memory

-54.5MiB live, 16.8MiB allocated; 38ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	81	4	85

Accuracy

100.0%

Counts

85 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.4%	#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 112 to 56 computations (50% saved)

regimes7.0ms (0.4%)

Memory

18.7MiB live, 18.7MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
#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)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x))))

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

Calls

4 calls:

2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
2.0ms	(-.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 15 to 12 computations (20% saved)

regimes5.0ms (0.3%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

#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)))

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

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 15 to 12 computations (20% saved)

regimes8.0ms (0.4%)

Memory

-35.9MiB live, 12.5MiB allocated; 7ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
#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)))

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

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 x x)`
99.4%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.4%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.4%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes4.0ms (0.2%)

Memory

10.7MiB live, 10.7MiB 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	`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)))`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify54.0ms (3.1%)

Memory

-2.5MiB live, 43.2MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	34	42
2	70	42
3	113	42
4	163	42
5	367	42
6	2781	42
7	6925	42

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations7.0ms (0.4%)

Memory

19.0MiB live, 19.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 42 to 18 computations (57.1% saved)

preprocess59.0ms (3.4%)

Memory: -5.0MiB live, 41.7MiB allocated; 4ms collecting garbage
Remove: (abs x)
Compiler: Compiled 156 to 78 computations (50% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0.1%)

sample855.0ms (49.3%)

explain59.0ms (3.4%)

preprocess247.0ms (14.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series3.0ms (0.2%)

rewrite49.0ms (2.8%)

eval8.0ms (0.5%)

prune2.0ms (0.1%)

series5.0ms (0.3%)

rewrite62.0ms (3.6%)

eval9.0ms (0.5%)

prune4.0ms (0.2%)

series5.0ms (0.3%)

rewrite84.0ms (4.8%)

eval42.0ms (2.4%)

prune3.0ms (0.2%)

series4.0ms (0.2%)

rewrite104.0ms (6%)

eval8.0ms (0.5%)

prune38.0ms (2.2%)

regimes7.0ms (0.4%)

regimes5.0ms (0.3%)

regimes8.0ms (0.4%)

regimes4.0ms (0.2%)

simplify54.0ms (3.1%)

derivations7.0ms (0.4%)

preprocess59.0ms (3.4%)

end0.0ms (0%)

Profiling