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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

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)

sample745.0ms (12%)

Memory

-19.1MiB live, 864.4MiB allocated

Samples

453.0ms	8 256×	0	valid
0.0ms	5×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 253.0ms

ival-mult: 121.0ms (47.9% of total)

ival-sqrt: 68.0ms (26.9% of total)

ival-sub: 49.0ms (19.4% of total)

ival-true: 6.0ms (2.4% of total)

exact: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain73.0ms (1.2%)

Memory

-3.9MiB live, 72.1MiB allocated

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

29.0ms

512×

valid

Compiler

Compiled 58 to 24 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 11.0ms (59.5% of total)

ival-sqrt: 4.0ms (21.6% of total)

ival-sub: 3.0ms (16.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess383.0ms (6.2%)

Memory

28.9MiB live, 296.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	25	13
2	45	13
3	87	13
4	116	13
5	167	13
6	280	13
7	507	13
8	900	13
9	1467	13
10	3839	13
11	5537	13
12	6300	13
13	6598	13
14	6654	13
15	6686	13
16	6948	13
17	7542	13
0	5	6
0	8	6
1	15	6
2	22	6
3	30	6
4	45	6
5	65	6
6	108	6
7	305	6
8	585	6
9	1159	6
10	2070	6
11	3779	6
12	4733	6
13	5051	6
14	5337	6
15	5506	6
16	5583	6
17	5850	6
18	6848	6
19	7904	6
0	8289	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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

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)

simplify314.0ms (5.1%)

Memory

-38.1MiB live, 331.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	15	16
2	22	16
3	30	16
4	45	16
5	65	16
6	108	16
7	305	16
8	585	16
9	1159	16
10	2070	16
11	3779	16
12	4733	16
13	5051	16
14	5337	16
15	5506	16
16	5583	16
17	5850	16
18	6848	16
19	7904	16
0	8289	16

Stop Event

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

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
(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

localize15.0ms (0.2%)

Memory

32.3MiB live, 32.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Samples

11.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (36.8% of total)

ival-sqrt: 2.0ms (36.8% of total)

ival-sub: 1.0ms (18.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())

#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 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)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify136.0ms (2.2%)

Memory

-26.6MiB live, 130.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	295
1	149	286
2	419	278
3	1279	264
4	3834	263
5	6189	263
0	8166	252

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* 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))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -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)))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite158.0ms (2.5%)

Memory

1.8MiB live, 200.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	32	14
2	187	14
3	1340	14
0	9365	12

Stop Event

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

Counts

3 → 355

Calls

Call 1

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

Outputs
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eval95.0ms (1.5%)

Memory: 13.3MiB live, 133.7MiB allocated
Compiler: Compiled 9 639 to 1 265 computations (86.9% saved)

prune87.0ms (1.4%)

Memory

-14.9MiB live, 23.6MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	387	4	391
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	387	5	392

Accuracy

100.0%

Counts

392 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
▶	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	98.7%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	98.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 53 to 35 computations (34% saved)

simplify238.0ms (3.8%)

Memory

40.1MiB live, 187.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (neg.f64 x) x #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
cost-diff	1536	(/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
cost-diff	6592	(-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
cost-diff	0	(pow.f64 x #s(literal 4 binary64))
cost-diff	0	(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	175
0	40	143
1	79	143
2	174	139
3	596	138
4	2532	137
5	7378	137
0	8294	137

Stop Event

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

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

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)))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #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))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#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 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 1 binary64)
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
(fma.f64 x x #s(literal 1 binary64))
(sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (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 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (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 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) x #s(literal -1 binary64))
(neg.f64 x)
x
#s(literal -1 binary64)
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))))
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)

localize249.0ms (4%)

Memory

-34.3MiB live, 134.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
accuracy	0.01171875	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))
accuracy	0.015625	(/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
accuracy	0.015625	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
accuracy	0	(pow.f64 x #s(literal 4 binary64))
accuracy	0	(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
accuracy	0.0078125	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
accuracy	0.0234375	(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.8326502968621997	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	1.2816421136540954	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Samples

198.0ms

256×

valid

Compiler

Compiled 350 to 46 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 185.0ms

ival-sub: 68.0ms (36.8% of total)

ival-mult: 55.0ms (29.7% of total)

ival-sqrt: 50.0ms (27% of total)

ival-add: 4.0ms (2.2% of total)

ival-div: 3.0ms (1.6% of total)

ival-pow: 2.0ms (1.1% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

series14.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

14 → 168

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (patch (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (patch (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 4))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (patch (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (pow x 2)) 1) (taylor 0 x) (#s(alt (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (patch (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (pow x 2) 1)) 1) (taylor 0 x) (#s(alt (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (patch (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1) (taylor 0 x) (#s(alt (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (patch (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (patch (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (patch (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (patch (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (patch (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -2 (pow x 2)) 1) (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1) (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1) (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (/ (- 1 (pow x 4)) (+ (* x x) 1))) (/ (- 1 (pow x 4)) (+ (* x x) 1)) (- 1 (pow x 4)) (pow x 4) (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (/ (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (* (+ (* (neg x) x) -1) (+ (* x x) 1))) (sqrt (/ (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (* (+ (* (neg x) x) -1) (+ (* x x) 1)))) (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (+ (* x x) 1)) (* (+ (* (neg x) x) -1) (pow x 4)))
2.0ms	x	@	-inf	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (/ (- 1 (pow x 4)) (+ (* x x) 1))) (/ (- 1 (pow x 4)) (+ (* x x) 1)) (- 1 (pow x 4)) (pow x 4) (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (/ (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (* (+ (* (neg x) x) -1) (+ (* x x) 1))) (sqrt (/ (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (* (+ (* (neg x) x) -1) (+ (* x x) 1)))) (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (+ (* x x) 1)) (* (+ (* (neg x) x) -1) (pow x 4)))
2.0ms	x	@	0	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (/ (- 1 (pow x 4)) (+ (* x x) 1))) (/ (- 1 (pow x 4)) (+ (* x x) 1)) (- 1 (pow x 4)) (pow x 4) (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (/ (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (* (+ (* (neg x) x) -1) (+ (* x x) 1))) (sqrt (/ (- (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (pow x 4))) (* (+ (* (neg x) x) -1) (+ (* x x) 1)))) (+ (* (neg x) x) -1) (* (+ (* (neg x) x) -1) (+ (* x x) 1)) (* (+ (* (neg x) x) -1) (pow x 4)))

Time

Variable

Point

Expression

4.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify190.0ms (3.1%)

Memory

2.4MiB live, 114.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	1819
1	431	1677
2	1484	1631
3	6040	1619
0	8178	1570

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
1
(+ 1 (* -1 (pow x 4)))
(+ 1 (* -1 (pow x 4)))
(+ 1 (* -1 (pow x 4)))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (pow x 2) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1)
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
-1
(- (* -1 (pow x 2)) 1)
(- (* -1 (pow x 2)) 1)
(- (* -1 (pow x 2)) 1)
-1
(- (* -2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(* -1 (pow x 4))
(* (pow x 4) (- (* -1 (pow x 2)) 1))
(* (pow x 4) (- (* -1 (pow x 2)) 1))
(* (pow x 4) (- (* -1 (pow x 2)) 1))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* 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))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* 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))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* 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))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 4))
(* (pow x 4) (- (/ 1 (pow x 4)) 1))
(* (pow x 4) (- (/ 1 (pow x 4)) 1))
(* (pow x 4) (- (/ 1 (pow x 4)) 1))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* x (sqrt -1))
(* x (- (+ (sqrt -1) (* -1 (/ (sqrt -1) (pow x 2)))) (/ 1/2 (* (pow x 2) (sqrt -1)))))
(* x (- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ (sqrt -1) (pow x 4)))))) (/ 1/2 (* (pow x 2) (sqrt -1)))))
(* x (- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (/ (- 1 (* -1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ (sqrt -1) (pow x 4))))))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1/2 (* (pow x 6) (sqrt -1))))))
(* -1 (pow x 2))
(* -1 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))
(* -1 (pow x 4))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* -1 (pow x 6))
(* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -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)))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -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)))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -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)))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 4))
(* (pow x 4) (- (/ 1 (pow x 4)) 1))
(* (pow x 4) (- (/ 1 (pow x 4)) 1))
(* (pow x 4) (- (/ 1 (pow x 4)) 1))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (- (+ (sqrt -1) (* -1 (/ (sqrt -1) (pow x 2)))) (/ 1/2 (* (pow x 2) (sqrt -1))))))
(* -1 (* x (- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ (sqrt -1) (pow x 4)))))) (/ 1/2 (* (pow x 2) (sqrt -1))))))
(* -1 (* x (- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (/ (- 1 (* -1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (/ (- 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ (sqrt -1) (pow x 4))))))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1/2 (* (pow x 6) (sqrt -1)))))))
(* -1 (pow x 2))
(* -1 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))))
(* -1 (pow x 4))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* -1 (pow x 6))
(* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 6) (+ 1 (/ 1 (pow x 2)))))

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

rewrite279.0ms (4.5%)

Memory

-49.8MiB live, 262.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	151
0	40	99
1	176	99
2	1423	97
0	8864	97

Stop Event

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

Counts

14 → 1 369

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)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
(sqrt.f64 (/.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) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
(-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(fma.f64 (neg.f64 x) x #s(literal -1 binary64))
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))

Outputs
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eval357.0ms (5.7%)

Memory: 53.2MiB live, 582.3MiB allocated
Compiler: Compiled 65 469 to 5 331 computations (91.9% saved)

prune99.0ms (1.6%)

Memory

-31.9MiB live, 106.0MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 782	2	1 784
Fresh	0	0	0
Picked	2	2	4
Done	0	1	1
Total	1 784	5	1 789

Accuracy

100.0%

Counts

1 789 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
▶	100.0%	(sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	98.7%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	98.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 61 to 36 computations (41% saved)

simplify227.0ms (3.7%)

Memory

16.2MiB live, 293.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
cost-diff	256	(neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
cost-diff	704	(fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (*.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
cost-diff	1536	(/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	176
0	33	142
1	73	131
2	192	113
3	596	110
4	1634	110
5	4184	110
6	6138	110
7	6884	110
8	7412	110
9	7623	110
10	7697	110
0	8139	109

Stop Event

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

Calls

Call 1

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

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

localize56.0ms (0.9%)

Memory

9.5MiB live, 166.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
accuracy	0.015625	(/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
accuracy	0.015625	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
accuracy	0.01953125	(.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0	(neg.f64 x)
accuracy	0.0078125	(sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
accuracy	0.0234375	(/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))

Samples

41.0ms

256×

valid

Compiler

Compiled 379 to 38 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 11.0ms (43.1% of total)

ival-add: 5.0ms (19.6% of total)

ival-sqrt: 4.0ms (15.7% of total)

ival-div: 3.0ms (11.8% of total)

ival-neg: 2.0ms (7.8% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.2%)

Memory

-5.8MiB live, 32.6MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (pow x 2) 1)) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -2 (pow x 2)) 1) (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1) (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1) (taylor 0 x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow x 6) (taylor -inf x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4))))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4))))))))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) (patch (.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

6.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify258.0ms (4.2%)

Memory

-0.0MiB live, 274.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	136	1185
1	394	1080
2	1229	1038
3	5825	1033
0	8760	984

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (pow x 2) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1)
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (pow x 2)))
(* (pow x 2) (+ 1 (pow x 2)))
(* (pow x 2) (+ 1 (pow x 2)))
-1
(- (* -2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* 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))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2))))))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4))))))))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4))))))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 4)
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* -1 (pow x 4))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -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)))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4)))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4)))))))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 4)
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* -1 (pow x 4))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(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))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(fma.f64 (neg.f64 x) x #s(literal -1 binary64))
(- (* (pow x 2) (- (pow x 2) 1)) 1)
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal -1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (pow x 2)))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 2) (+ 1 (pow x 2)))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 2) (+ 1 (pow x 2)))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
-1
#s(literal -1 binary64)
(- (* -2 (pow x 2)) 1)
(fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) (*.f64 x x) #s(literal -1 binary64))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1 binary64) (.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64)))) x))
(* 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))))))
(.f64 (-.f64 (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64)))) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x)
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4))))))))
(.f64 (+.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4))))))))))))
(.f64 (+.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal -5/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)) (+.f64 (fma.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) x) x)
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (sqrt.f64 #s(literal -1 binary64)))) x)
(* -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)))))))
(.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2)))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4)))))))))
(.f64 (+.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4)))))))))))))
(.f64 (-.f64 (-.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal -5/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)) (+.f64 (fma.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 #s(literal -1 binary64))) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) x) x)
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))

rewrite150.0ms (2.4%)

Memory

-5.6MiB live, 267.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	144
0	33	121
1	144	73
2	1247	54
0	9918	52

Stop Event

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

Counts

11 → 1 327

Calls

Call 1

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

Outputs
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eval288.0ms (4.6%)

Memory: 3.3MiB live, 401.4MiB allocated
Compiler: Compiled 51 265 to 4 306 computations (91.6% saved)

prune26.0ms (0.4%)

Memory

5.3MiB live, 93.2MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 610	2	1 612
Fresh	0	0	0
Picked	2	0	2
Done	0	3	3
Total	1 612	5	1 617

Accuracy

100.0%

Counts

1 617 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	100.0%	(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
✓	98.7%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	98.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify154.0ms (2.5%)

Memory

1.5MiB live, 192.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
cost-diff	704	(fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (*.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
cost-diff	1536	(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
cost-diff	128	(neg.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff	192	(*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	138
0	33	138
1	69	138
2	170	126
3	442	113
4	1164	91
5	3441	87
6	6450	87
0	8114	86

Stop Event

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

Calls

Call 1

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

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

localize49.0ms (0.8%)

Memory

27.9MiB live, 65.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
accuracy	0.015625	(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
accuracy	0.015625	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
accuracy	0.01953125	(.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x))
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(neg.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.0078125	(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
accuracy	0.01171875	(*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))

Samples

36.0ms

256×

valid

Compiler

Compiled 296 to 38 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 9.0ms (38.2% of total)

ival-add: 5.0ms (21.2% of total)

ival-sqrt: 4.0ms (17% of total)

ival-div: 2.0ms (8.5% of total)

ival-neg: 2.0ms (8.5% of total)

ival-sub: 1.0ms (4.2% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

-24.9MiB live, 13.0MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (neg.f64 (-.f64 x #s(literal 1 binary64))) (patch (neg.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (patch (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (.f64 x x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (neg.f64 (-.f64 x #s(literal 1 binary64))) (patch (neg.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (neg.f64 (-.f64 x #s(literal 1 binary64))) (patch (neg.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (neg.f64 (-.f64 x #s(literal 1 binary64))) (patch (neg.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (neg.f64 (-.f64 x #s(literal 1 binary64))) (patch (neg.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify249.0ms (4%)

Memory

-2.4MiB live, 214.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	146	1148
1	422	1034
2	1290	989
3	6258	978
0	8193	926

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 118

Calls

Call 1

Inputs
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (pow x 2) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (pow x 2)))
(* (pow x 2) (+ 1 (pow x 2)))
(* (pow x 2) (+ 1 (pow x 2)))
-1
(- (* -2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* 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))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2))))))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4))))))))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4))))))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* -1 (pow x 4))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -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)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4)))))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4)))))))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* -1 (pow x 4))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(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))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(fma.f64 (neg.f64 x) x #s(literal -1 binary64))
(- (* (pow x 2) (- (pow x 2) 1)) 1)
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal -1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (+ 1 (pow x 2))) 1)) 1)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(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))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (pow x 2)))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 2) (+ 1 (pow x 2)))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 2) (+ 1 (pow x 2)))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
-1
#s(literal -1 binary64)
(- (* -2 (pow x 2)) 1)
(fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (- (* -1 (pow x 2)) 2)) 1)
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) (*.f64 x x) #s(literal -1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* 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))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2))))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4))))))))
(.f64 (+.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4))))))))))))
(.f64 (+.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal -5/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)) (+.f64 (fma.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) x) x)
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) x (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))))
(* -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)))))))
(neg.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 4))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1 (+ (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* x (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (* 1/2 (/ (sqrt -1) (pow x 2)))))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x)))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (/ (sqrt -1) (pow x 4)))))))))
(.f64 (+.f64 (fma.f64 #s(literal -9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) (pow x 2))) (+ (* -1 (/ (sqrt -1) (pow x 6))) (+ (* -5/8 (/ (sqrt -1) (pow x 4))) (+ (* -1/2 (/ (sqrt -1) (pow x 4))) (+ (* -3/16 (/ (sqrt -1) (pow x 6))) (+ (* 1/2 (/ (sqrt -1) (pow x 2))) (+ (* 1/2 (/ (sqrt -1) (pow x 6))) (+ (* 5/8 (/ (sqrt -1) (pow x 6))) (/ (sqrt -1) (pow x 4)))))))))))))
(.f64 (+.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal -5/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)) (+.f64 (fma.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 9/8 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 4) (+ 1 (* 2 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal -2 binary64)) x) x)
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))

rewrite207.0ms (3.3%)

Memory

22.8MiB live, 214.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	120
0	33	120
1	135	106
2	1111	86
0	9417	83

Stop Event

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

Counts

10 → 954

Calls

Call 1

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

Outputs
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eval220.0ms (3.6%)

Memory: -1.2MiB live, 344.4MiB allocated
Compiler: Compiled 36 659 to 4 055 computations (88.9% saved)

prune27.0ms (0.4%)

Memory

-2.8MiB live, 80.5MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 155	2	1 157
Fresh	0	0	0
Picked	2	0	2
Done	0	3	3
Total	1 157	5	1 162

Accuracy

100.0%

Counts

1 162 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(sqrt.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) (neg.f64 x) (-.f64 x #s(literal -1 binary64))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
	100.0%	(sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
✓	98.7%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	98.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 188 to 74 computations (60.6% saved)

regimes14.0ms (0.2%)

Memory

2.2MiB live, 41.1MiB allocated

Counts

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

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

Calls

4 calls:

4.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes9.0ms (0.1%)

Memory

-11.1MiB live, 28.1MiB allocated

Counts

5 → 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 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))

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

Calls

4 calls:

2.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes5.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

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:

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes5.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

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
98.0%	1	`x`
98.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
98.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
98.0%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify28.0ms (0.4%)

Memory

-26.1MiB live, 56.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	28	37
2	37	37
3	41	37
4	43	37

Stop Event

1×

saturated

Calls

Call 1

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

soundness740.0ms (11.9%)

Memory

3.5MiB live, 647.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	120
0	33	120
1	135	106
2	1111	86
0	9417	83
0	17	144
0	33	121
1	144	73
2	1247	54
0	9918	52
0	24	151
0	40	99
1	176	99
2	1423	97
0	8864	97
0	5	14
0	8	14
1	32	14
2	187	14
3	1340	14
0	9365	12
0	62	295
1	149	286
2	419	278
3	1279	264
4	3834	263
5	6189	263
0	8166	252

Stop Event

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

Compiler

Compiled 129 to 71 computations (45% saved)

preprocess36.0ms (0.6%)

Memory: 12.8MiB live, 88.1MiB allocated
Remove: (abs x)
Compiler: Compiled 102 to 62 computations (39.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample745.0ms (12%)

explain73.0ms (1.2%)

preprocess383.0ms (6.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify314.0ms (5.1%)

localize15.0ms (0.2%)

series3.0ms (0%)

simplify136.0ms (2.2%)

rewrite158.0ms (2.5%)

eval95.0ms (1.5%)

prune87.0ms (1.4%)

simplify238.0ms (3.8%)

localize249.0ms (4%)

series14.0ms (0.2%)

simplify190.0ms (3.1%)

rewrite279.0ms (4.5%)

eval357.0ms (5.7%)

prune99.0ms (1.6%)

simplify227.0ms (3.7%)

localize56.0ms (0.9%)

series14.0ms (0.2%)

simplify258.0ms (4.2%)

rewrite150.0ms (2.4%)

eval288.0ms (4.6%)

prune26.0ms (0.4%)

simplify154.0ms (2.5%)

localize49.0ms (0.8%)

series10.0ms (0.2%)

simplify249.0ms (4%)

rewrite207.0ms (3.3%)

eval220.0ms (3.6%)

prune27.0ms (0.4%)

regimes14.0ms (0.2%)

regimes9.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

simplify28.0ms (0.4%)

soundness740.0ms (11.9%)

preprocess36.0ms (0.6%)

end0.0ms (0%)

Profiling