Metrics for Asymptote A

start0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated

analyze2.0ms (0%)

Memory

4.4MiB live, 4.4MiB 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
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.4s (23.8%)

Memory

49.3MiB live, 1 274.0MiB allocated

Samples

675.0ms	3 810×	1	valid
291.0ms	4 446×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 704.0ms

ival-div: 234.0ms (33.2% of total)

ival-sub: 226.0ms (32.1% of total)

adjust: 126.0ms (17.9% of total)

ival-add: 103.0ms (14.6% of total)

ival-true: 7.0ms (1% of total)

exact: 5.0ms (0.7% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain146.0ms (2.5%)

Memory

-44.2MiB live, 164.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
64	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`
0	-	-	`(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))`
0	-	-	`(-.f64 x #s(literal 1 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`	cancellation	64	0

Confusion

	Predicted +	Predicted -
+	64	0
-	0	192

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	64	0	0
-	0	0	192

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	192
1	64

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms	238×	1	valid
15.0ms	274×	0	valid

Compiler

Compiled 73 to 25 computations (65.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-div: 10.0ms (36.1% of total)

ival-sub: 7.0ms (25.3% of total)

adjust: 5.0ms (18.1% of total)

ival-add: 4.0ms (14.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess27.0ms (0.5%)

Memory

13.1MiB live, 51.0MiB allocated

Algorithm

1×	egg-herbie

Rules

160×	`lower-fma.f64`
160×	`lower-fma.f32`
96×	`lower-*.f64`
96×	`lower-*.f32`
72×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	21	25
2	52	22
3	106	22
4	190	22
5	258	22
6	273	22
7	275	22
0	7	11
0	12	11
1	20	11
2	27	11
3	40	11
4	61	11
5	86	11
6	131	11
7	174	11
8	243	11
9	280	11
10	300	11
11	300	11
0	300	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs

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

(-.f64 (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1 binary64))))

Symmetry

(abs x)

Compiler

Compiled 11 to 7 computations (36.4% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.0%	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify11.0ms (0.2%)

Memory

21.5MiB live, 21.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

160×	`lower-fma.f64`
160×	`lower-fma.f32`
96×	`lower-*.f64`
96×	`lower-*.f32`
72×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
0	12	29
1	20	29
2	27	29
3	40	29
4	61	29
5	86	29
6	131	29
7	174	29
8	243	29
9	280	29
10	300	29
11	300	29
0	300	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64)))
#s(literal 1 binary64)
(+.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal -1 binary64))
x
(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

localize34.0ms (0.6%)

Memory

-22.3MiB live, 60.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
accuracy	14.057570463067725	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Samples

21.0ms	119×	1	valid
7.0ms	137×	0	valid

Compiler

Compiled 31 to 9 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

adjust: 9.0ms (43.9% of total)

ival-div: 5.0ms (24.4% of total)

ival-sub: 3.0ms (14.6% of total)

ival-add: 2.0ms (9.8% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/ 1 (+ x 1)) (+ x 1) (/ 1 (- x 1)))

0.0ms

((- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/ 1 (+ x 1)) (+ x 1) (/ 1 (- x 1)))

0.0ms

-inf

((- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/ 1 (+ x 1)) (+ x 1) (/ 1 (- x 1)))

simplify124.0ms (2.1%)

Memory

28.1MiB live, 177.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10 646×	`lower-fma.f64`
10 646×	`lower-fma.f32`
3 680×	`lower-*.f64`
3 680×	`lower-*.f32`
1 938×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	405
1	220	395
2	557	373
3	1750	352
4	5230	352
0	8132	343

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

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

Outputs
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- x 1)))
(fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
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 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* x (- (* -1 x) 1)) 1)
(fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64))
(- (* x (- (* x (- (* -1 x) 1)) 1)) 1)
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))) x) x)
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) x) x) (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1 binary64)) x) #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 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (/ 1 x)) x)
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) #s(literal -1 binary64)) x)
(/ (+ 1 (+ (/ 1 x) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) x)
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))) x) x)
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) x) x) (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1 binary64)) x) #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 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (/ 1 x)) x)
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) #s(literal -1 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)) x)

rewrite192.0ms (3.3%)

Memory

-29.6MiB live, 286.4MiB allocated

Rules

10 498×	`lower-fma.f64`
10 498×	`lower-fma.f32`
3 964×	`lower-*.f64`
3 964×	`lower-*.f32`
3 924×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
0	12	24
1	66	24
2	644	24
0	9039	22

Stop Event

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

Counts

4 → 702

Calls

Call 1

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

Outputs
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eval103.0ms (1.8%)

Memory: 16.7MiB live, 235.7MiB allocated
Compiler: Compiled 19 147 to 2 021 computations (89.4% saved)

prune23.0ms (0.4%)

Memory

10.2MiB live, 56.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	742	6	748
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	743	6	749

Accuracy

100.0%

Counts

749 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.8%	(/.f64 (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
▶	81.8%	(/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
▶	52.7%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)))
	48.4%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))) x) x))
▶	47.9%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
▶	53.2%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

Compiler

Compiled 108 to 80 computations (25.9% saved)

simplify216.0ms (3.7%)

Memory

-4.1MiB live, 265.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
cost-diff	192	(-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64))
cost-diff	384	(-.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal -2 binary64) (*.f64 x x))
cost-diff	0	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))
cost-diff	0	(/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))
cost-diff	192	(-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64))
cost-diff	384	(-.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	704	(/.f64 (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))

Rules

23 032×	`lower-fma.f32`
23 028×	`lower-fma.f64`
4 068×	`lower-*.f32`
4 066×	`lower-*.f64`
3 502×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	154
0	38	171
1	71	171
2	159	119
3	460	98
4	1162	98
5	3184	98
6	4344	98
7	5009	98
8	5395	98
9	5635	98
10	5712	98
0	8367	98

Stop Event

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

Calls

Call 1

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

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

localize365.0ms (6.2%)

Memory

-19.9MiB live, 164.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64))
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0.3102202966978304	(/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
accuracy	28.577475276210787	(-.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	0	(*.f64 x x)
accuracy	0.3492827966978304	(/.f64 #s(literal -2 binary64) (*.f64 x x))
accuracy	33.06372650733475	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
accuracy	0	(*.f64 x x)
accuracy	30.269341504044625	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)))
accuracy	29.97005101532339	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))
accuracy	0	(-.f64 #s(literal -1 binary64) x)
accuracy	0.00390625	(/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))
accuracy	0.046875	(/.f64 (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
accuracy	28.577475276210787	(-.f64 (-.f64 x #s(literal 1 binary64)) x)

Samples

43.0ms	121×	1	valid
19.0ms	135×	0	valid

Compiler

Compiled 144 to 24 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-div: 14.0ms (34.6% of total)

ival-sub: 9.0ms (22.2% of total)

adjust: 6.0ms (14.8% of total)

ival-add: 5.0ms (12.3% of total)

ival-mult: 5.0ms (12.3% of total)

exact: 1.0ms (2.5% of total)

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

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

series9.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

13 → 156

Calls

Call 1

Inputs
#s(alt (/.f64 (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (patch (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64)) (patch #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))) (patch #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (.f64 x x))) (patch #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -2 binary64) (.f64 x x)) (patch (/.f64 #s(literal -2 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (patch (/.f64 (-.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64)) (fma.f64 x 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 #s(literal -1 binary64) x) (patch (-.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

simplify137.0ms (2.3%)

Memory

11.4MiB live, 163.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 048×	`lower-fma.f64`
14 048×	`lower-fma.f32`
4 002×	`lower-*.f64`
4 002×	`lower-*.f32`
1 726×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	1167
1	217	1159
2	568	1076
3	1644	1034
4	4535	1034
0	8436	995

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 154

Calls

Call 1

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

Outputs
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)))
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
2
#s(literal 2 binary64)
(+ 2 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64))
(+ 2 (* x (- (* 2 x) 2)))
(fma.f64 (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (- (* x (+ 2 (* -2 x))) 2)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 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)
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)))
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
(- x 1)
(-.f64 x #s(literal 1 binary64))
(- x 1)
(-.f64 x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 2 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/ (- (+ 2 (/ 2 (pow x 2))) (* 2 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 2 (pow x 2))) (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3))))) x)
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
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 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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 2 (/ 1 x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 2) x))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -2 binary64)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))))
x
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 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)

rewrite177.0ms (3%)

Memory

-18.0MiB live, 220.7MiB allocated

Rules

5 016×	`lower-/.f32`
5 008×	`lower-/.f64`
4 184×	`lower-*.f32`
4 182×	`lower-*.f64`
3 080×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	118
0	38	121
1	203	113
2	1949	113
0	8661	108

Stop Event

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

Counts

13 → 1 056

Calls

Call 1

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

Outputs
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval224.0ms (3.8%)

Memory: 36.3MiB live, 415.6MiB allocated
Compiler: Compiled 49 732 to 4 371 computations (91.2% saved)

prune38.0ms (0.6%)

Memory

-12.1MiB live, 110.3MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1 753	5	1 758
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	1 756	8	1 764

Accuracy

100.0%

Counts

1 764 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 (/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
▶	54.8%	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x))
▶	99.5%	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
▶	48.3%	#s(approx (/ (/ (- (- (- x 1) x) 1) (- -1 x)) (- 1 x)) (/.f64 (/.f64 #s(literal -2 binary64) x) x))
✓	52.7%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)))
✓	47.9%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
▶	48.3%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)))
✓	53.2%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

Compiler

Compiled 85 to 75 computations (11.8% saved)

simplify179.0ms (3%)

Memory

20.4MiB live, 170.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal -2 binary64))
cost-diff	0	(*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64))
cost-diff	0	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)))
cost-diff	0	(/.f64 #s(literal -2 binary64) x)
cost-diff	0	(/.f64 (/.f64 #s(literal -2 binary64) x) x)
cost-diff	0	#s(approx (/ (/ (- (- (- x 1) x) 1) (- -1 x)) (- 1 x)) (/.f64 (/.f64 #s(literal -2 binary64) x) x))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	#s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64))
cost-diff	0	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(literal -1 binary64) x)
cost-diff	0	#s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64))
cost-diff	0	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x))
cost-diff	704	(/.f64 (/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))

Rules

18 554×	`lower-fma.f32`
18 552×	`lower-fma.f64`
2 444×	`lower-*.f32`
2 442×	`lower-*.f64`
2 346×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	173
0	43	176
1	68	176
2	142	128
3	367	119
4	872	114
5	3129	114
6	5484	114
7	6977	114
8	7870	114
0	8106	114

Stop Event

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

Calls

Call 1

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

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

localize139.0ms (2.4%)

Memory

-23.7MiB live, 160.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal -2 binary64))
accuracy	0.00390625	(*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64))
accuracy	33.06372650733475	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)))
accuracy	0	(/.f64 #s(literal -2 binary64) x)
accuracy	0.10546875	(/.f64 (/.f64 #s(literal -2 binary64) x) x)
accuracy	33.06372650733475	#s(approx (/ (/ (- (- (- x 1) x) 1) (- -1 x)) (- 1 x)) (/.f64 (/.f64 #s(literal -2 binary64) x) x))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	#s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64))
accuracy	0.3102202966978304	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.046875	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x))
accuracy	29.348855217494446	#s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64))
accuracy	0	(-.f64 #s(literal -1 binary64) x)
accuracy	0	#s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64))
accuracy	0.00390625	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x))
accuracy	0.046875	(/.f64 (/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))

Samples

76.0ms	121×	1	valid
24.0ms	135×	0	valid

Compiler

Compiled 151 to 25 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-div: 36.0ms (44.8% of total)

ival-sub: 26.0ms (32.3% of total)

adjust: 6.0ms (7.5% of total)

ival-add: 5.0ms (6.2% of total)

ival-mult: 4.0ms (5% of total)

ival-pow: 3.0ms (3.7% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

15 → 180

Calls

Call 1

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

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

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify146.0ms (2.5%)

Memory

-9.4MiB live, 177.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 040×	`lower-fma.f64`
14 040×	`lower-fma.f32`
4 626×	`lower-*.f64`
4 626×	`lower-*.f32`
1 706×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	1376
1	215	1351
2	565	1264
3	1629	1220
4	4959	1220
0	8161	1176

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

Outputs
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64))
(+ 2 (* x (- (* 2 x) 2)))
(fma.f64 (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (- (* x (+ 2 (* -2 x))) 2)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)))
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64))
(+ 2 (* x (- (* 2 x) 2)))
(fma.f64 (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (- (* x (+ 2 (* -2 x))) 2)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) x #s(literal 2 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)
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
2
#s(literal 2 binary64)
(+ 2 (* 2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 2 (* (pow x 2) (+ 2 (* 2 (pow x 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64) #s(literal 2 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 2 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/ (- (+ 2 (/ 2 (pow x 2))) (* 2 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 2 (pow x 2))) (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3))))) x)
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)))
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 2 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/ (- (+ 2 (/ 2 (pow x 2))) (* 2 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x) #s(literal -2 binary64)) x)
(/ (- (+ 2 (/ 2 (pow x 2))) (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3))))) x)
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)))
(* -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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 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))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 2 (/ 1 x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 2) x))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)))
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 binary64)
-2
#s(literal -2 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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 2 (/ 1 x)) 2) x))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x) #s(literal -2 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 2) x))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)))
(* -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)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 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))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 2))) 2) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) (*.f64 x x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 (pow x 2)))) (pow x 4))) (+ 2 (* 2 (/ 1 (pow x 2))))) (pow x 2))
(*.f64 (/.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64)) x) x) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ -2 (pow x 2))
(/.f64 (/.f64 #s(literal -2 binary64) x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

rewrite151.0ms (2.6%)

Memory

3.4MiB live, 245.0MiB allocated

Rules

5 152×	`lower-/.f32`
5 140×	`lower-/.f64`
4 276×	`lower-*.f32`
4 274×	`lower-*.f64`
3 014×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	147
0	43	154
1	212	140
2	1950	140
0	8618	138

Stop Event

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

Counts

15 → 438

Calls

Call 1

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

Outputs
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eval96.0ms (1.6%)

Memory: 19.1MiB live, 175.1MiB allocated
Compiler: Compiled 8 748 to 1 194 computations (86.4% saved)

prune20.0ms (0.3%)

Memory

-7.3MiB live, 63.5MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	690	2	692
Fresh	0	0	0
Picked	2	3	5
Done	0	3	3
Total	692	8	700

Accuracy

100.0%

Counts

700 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	3.8%	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x)))
✓	99.5%	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
▶	99.5%	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x)))
✓	48.3%	#s(approx (/ (/ (- (- (- x 1) x) 1) (- -1 x)) (- 1 x)) (/.f64 (/.f64 #s(literal -2 binary64) x) x))
✓	52.7%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)))
✓	47.9%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
✓	48.3%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)))
✓	53.2%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify215.0ms (3.7%)

Memory

-13.6MiB live, 229.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (- 1 x) (neg.f64 x))
cost-diff	0	#s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x)))
cost-diff	0	(fma.f64 x x x)
cost-diff	0	#s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64))
cost-diff	0	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x)))
cost-diff	384	(+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x))

Rules

12 654×	`lower-fma.f32`
12 652×	`lower-fma.f64`
2 412×	`lower-*.f64`
2 412×	`lower-*.f32`
2 202×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	88
0	27	88
1	51	88
2	114	80
3	277	58
4	607	58
5	1799	58
6	3544	58
7	4707	58
8	5351	58
9	5737	58
10	5986	58
11	6049	58
12	6107	58
13	6986	58
0	8008	56

Stop Event

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

Calls

Call 1

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

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

localize50.0ms (0.8%)

Memory

21.4MiB live, 99.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.046875	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x)))
accuracy	29.348855217494446	#s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64))
accuracy	32.90007774728393	#s(approx (- 1 x) (neg.f64 x))
accuracy	0	(-.f64 #s(literal -1 binary64) x)
accuracy	0	#s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64))
accuracy	0.015625	(+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x))
accuracy	0.3102202966978304	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x)))

Samples

25.0ms	112×	1	valid
14.0ms	144×	0	valid

Compiler

Compiled 79 to 19 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sub: 8.0ms (28.7% of total)

ival-div: 6.0ms (21.6% of total)

adjust: 5.0ms (18% of total)

ival-add: 3.0ms (10.8% of total)

ival-mult: 3.0ms (10.8% of total)

ival-neg: 1.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

simplify175.0ms (3%)

Memory

5.9MiB live, 162.1MiB allocated

Algorithm

1×	egg-herbie

Rules

18 292×	`lower-fma.f64`
18 292×	`lower-fma.f32`
4 334×	`lower-*.f64`
4 334×	`lower-*.f32`
1 598×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	650
1	228	633
2	582	592
3	2243	574
4	5817	574
0	8107	541

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 107

Calls

Call 1

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

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

rewrite171.0ms (2.9%)

Memory

-17.0MiB live, 193.6MiB allocated

Rules

5 284×	`lower-*.f64`
5 284×	`lower-*.f32`
4 546×	`lower-/.f32`
4 542×	`lower-/.f64`
2 502×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	83
0	27	83
1	141	83
2	1354	83
0	8377	83

Stop Event

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

Counts

9 → 309

Calls

Call 1

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

Outputs
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eval48.0ms (0.8%)

Memory: 11.4MiB live, 87.6MiB allocated
Compiler: Compiled 11 237 to 1 316 computations (88.3% saved)

prune13.0ms (0.2%)

Memory

-5.2MiB live, 32.6MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	415	1	416
Fresh	0	0	0
Picked	1	1	2
Done	0	6	6
Total	416	8	424

Accuracy

100.0%

Counts

424 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	3.8%	(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x)))
✓	99.5%	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
	47.8%	(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (+.f64 (fma.f64 x x x) #s(approx (- -1 x) (neg.f64 x))))
✓	48.3%	#s(approx (/ (/ (- (- (- x 1) x) 1) (- -1 x)) (- 1 x)) (/.f64 (/.f64 #s(literal -2 binary64) x) x))
✓	52.7%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64)))
✓	47.9%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
✓	48.3%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)))
✓	53.2%	#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

Compiler

Compiled 179 to 93 computations (48% saved)

regimes11.0ms (0.2%)

Memory

-29.1MiB live, 15.7MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes6.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

-31.4MiB live, 7.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
54.8%	1	`x`
54.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

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

(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x)))

Outputs

(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x)))

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
55.1%	2	`x`
55.1%	2	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Accuracy

Total -0.3b remaining (-1.1%)

Threshold costs -0.3b (-1.1%)

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
53.2%	1	`x`
53.2%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2.0

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2.0

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify24.0ms (0.4%)

Memory

4.6MiB live, 43.9MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`+-commutative-binary64-+.f64`
18×	`sub-neg-binary64-neg.f64-+.f64--.f64`
10×	`neg-sub0-binary64--.f64-neg.f64`
10×	`neg-mul-1-binary64-*.f64-neg.f64`
8×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	180
1	57	180
2	70	180
3	86	180
4	93	180
5	95	180
6	96	180

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(if (<=.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 0 binary64)) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 0 binary64)) (/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x))) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))))
#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

Outputs
(/.f64 (/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (+.f64 (fma.f64 x x x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 #s(approx (- (- (- x 1) x) 1) #s(literal -2 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(if (<=.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 0 binary64)) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))))
(if (<=.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 0 binary64)) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (/.f64 #s(literal -2 binary64) (.f64 x x))) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))))
(/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 0 binary64)) (/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x))) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))))
(if (<=.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 0 binary64)) (/.f64 #s(approx (/ (- (- (- x 1) x) 1) (- -1 x)) #s(literal 2 binary64)) #s(approx (- 1 x) (neg.f64 x))) #s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 2 binary64))))
#s(approx (- (/ 1 (+ x 1)) (/ 1 (- x 1))) #s(literal 2 binary64))

soundness1.1s (18.7%)

Memory

38.5MiB live, 649.4MiB allocated

Rules

14 048×	`lower-fma.f64`
14 048×	`lower-fma.f32`
14 040×	`lower-fma.f64`
14 040×	`lower-fma.f32`
10 646×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	1167
1	217	1159
2	568	1076
3	1644	1034
4	4535	1034
0	8436	995
0	76	1376
1	215	1351
2	565	1264
3	1629	1220
4	4959	1220
0	8161	1176
0	7	24
0	12	24
1	66	24
2	644	24
0	9039	22
0	80	405
1	220	395
2	557	373
3	1750	352
4	5230	352
0	8132	343
0	31	147
0	43	154
1	212	140
2	1950	140
0	8618	138

Stop Event

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

Compiler

Compiled 241 to 137 computations (43.2% saved)

preprocess74.0ms (1.2%)

Memory: -24.1MiB live, 106.6MiB allocated
Remove: (abs x)
Compiler: Compiled 222 to 102 computations (54.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	9	27
1	21	25
2	52	22
3	106	22
4	190	22
5	258	22
6	273	22
7	275	22
0	7	11
0	12	11
1	20	11
2	27	11
3	40	11
4	61	11
5	86	11
6	131	11
7	174	11
8	243	11
9	280	11
10	300	11
11	300	11
0	300	11

Iter	Nodes	Cost
0	7	29
0	12	29
1	20	29
2	27	29
3	40	29
4	61	29
5	86	29
6	131	29
7	174	29
8	243	29
9	280	29
10	300	29
11	300	29
0	300	29

Iter	Nodes	Cost
0	9	27
1	21	25
2	52	22
3	106	22
4	190	22
5	258	22
6	273	22
7	275	22
0	7	11
0	12	11
1	20	11
2	27	11
3	40	11
4	61	11
5	86	11
6	131	11
7	174	11
8	243	11
9	280	11
10	300	11
11	300	11
0	300	11

Iter	Nodes	Cost
0	7	29
0	12	29
1	20	29
2	27	29
3	40	29
4	61	29
5	86	29
6	131	29
7	174	29
8	243	29
9	280	29
10	300	29
11	300	29
0	300	29

start0.0ms (0%)

analyze2.0ms (0%)

sample1.4s (23.8%)

explain146.0ms (2.5%)

preprocess27.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify11.0ms (0.2%)

localize34.0ms (0.6%)

series3.0ms (0%)

simplify124.0ms (2.1%)

rewrite192.0ms (3.3%)

eval103.0ms (1.8%)

prune23.0ms (0.4%)

simplify216.0ms (3.7%)

localize365.0ms (6.2%)

series9.0ms (0.1%)

simplify137.0ms (2.3%)

rewrite177.0ms (3%)

eval224.0ms (3.8%)

prune38.0ms (0.6%)

simplify179.0ms (3%)

localize139.0ms (2.4%)

series8.0ms (0.1%)

simplify146.0ms (2.5%)

rewrite151.0ms (2.6%)

eval96.0ms (1.6%)

prune20.0ms (0.3%)

simplify215.0ms (3.7%)

localize50.0ms (0.8%)

series4.0ms (0.1%)

simplify175.0ms (3%)

rewrite171.0ms (2.9%)

eval48.0ms (0.8%)

prune13.0ms (0.2%)

regimes11.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify24.0ms (0.4%)

soundness1.1s (18.7%)

preprocess74.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	27
1	21	25
2	52	22
3	106	22
4	190	22
5	258	22
6	273	22
7	275	22
0	7	11
0	12	11
1	20	11
2	27	11
3	40	11
4	61	11
5	86	11
6	131	11
7	174	11
8	243	11
9	280	11
10	300	11
11	300	11
0	300	11

Iter	Nodes	Cost
0	7	29
0	12	29
1	20	29
2	27	29
3	40	29
4	61	29
5	86	29
6	131	29
7	174	29
8	243	29
9	280	29
10	300	29
11	300	29
0	300	29