Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

1.1MiB live, 1.1MiB 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
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample526.0ms (8.4%)

Memory

51.2MiB live, 663.2MiB allocated

Samples

316.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-mult: 68.0ms (37.1% of total)

ival-div: 57.0ms (31.1% of total)

ival-add: 45.0ms (24.5% of total)

ival-true: 6.0ms (3.3% of total)

exact: 5.0ms (2.7% of total)

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

Bogosity

explain268.0ms (4.3%)

Memory

6.1MiB live, 82.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	n/o	62	0
↳	`(*.f64 x x)`	overflow	62
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	62

Confusion

	Predicted +	Predicted -
+	62	0
-	0	194

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	62	0	0
-	0	0	194

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	194
1	62

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

230.0ms

512×

valid

Compiler

Compiled 46 to 19 computations (58.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 189.0ms

ival-mult: 182.0ms (96.6% of total)

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

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

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

exact: 0.0ms (0% of total)

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

preprocess24.0ms (0.4%)

Memory

-11.8MiB live, 24.4MiB allocated

Algorithm

1×	egg-herbie

Rules

46×	`associate-l`
42×	`times-frac`
30×	`unsub-neg`
28×	`distribute-lft-neg-in`
26×	`distribute-neg-frac2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.4%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff	128	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Rules

4×	`lower-+.f32`
2×	`lift-+.f64`
2×	`lift-/.f64`
2×	`lower-fma.f64`
2×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	11	17
0	11	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.3%)

Memory

-20.4MiB live, 23.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	14.493507084287701	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

14.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-div: 2.0ms (40.8% of total)

ival-mult: 2.0ms (40.8% of total)

ival-add: 1.0ms (20.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

Calls

9 calls:

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

simplify193.0ms (3.1%)

Memory

26.2MiB live, 180.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
2 988×	`lower-*.f64`
2 988×	`lower-*.f32`
1 640×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	226
1	131	224
2	312	216
3	888	212
4	2381	210
5	5550	210
6	7627	210
0	8047	197

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 35

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite165.0ms (2.7%)

Memory

11.3MiB live, 276.6MiB allocated

Rules

4 942×	`lower-/.f32`
4 940×	`lower-/.f64`
4 762×	`lower-fma.f64`
4 762×	`lower-fma.f32`
3 572×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13

Stop Event

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

Counts

3 → 327

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(fma.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (.f64 x x) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(fma.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (.f64 (.f64 x x) x) x)))
(fma.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (.f64 (.f64 x x) x) x) (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))))
(fma.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))))
(+.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(+.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (.f64 x x)) (.f64 (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (.f64 (*.f64 x x) x) x)))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval127.0ms (2%)

Memory: -12.3MiB live, 92.5MiB allocated
Compiler: Compiled 12 336 to 1 054 computations (91.5% saved)

prune260.0ms (4.2%)

Memory

-22.5MiB live, 101.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	356	6	362
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	357	6	363

Accuracy

100.0%

Counts

363 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	28.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
▶	51.7%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
	65.2%	(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
▶	51.2%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	50.4%	#s(approx (/ x (+ (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x))

Compiler

Compiled 98 to 50 computations (49% saved)

simplify308.0ms (4.9%)

Memory

4.0MiB live, 160.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

11 798×	`lower-fma.f32`
11 796×	`lower-fma.f64`
3 048×	`lower--.f32`
3 046×	`lower--.f64`
2 210×	`lower-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	96
0	25	96
1	34	96
2	47	96
3	67	92
4	127	92
5	184	92
6	294	92
7	733	92
8	1414	92
9	2620	92
10	4544	92
11	5702	92
12	6504	92
13	7036	92
14	7331	92
15	7383	92
0	8180	92

Stop Event

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

Calls

Call 1

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

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

localize178.0ms (2.9%)

Memory

23.6MiB live, 59.7MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	14.493507084287701	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
accuracy	31.075898031670768	#s(approx (+ (* x x) 1) (*.f64 x x))
accuracy	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0.03125	(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
accuracy	31.74167271876838	#s(approx (/ x (+ (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x))
accuracy	14.493507084287701	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	30.8005749989777	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	31.22386086657065	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	14.493507084287701	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 82 to 10 computations (87.8% saved)

Precisions

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

ival-div: 3.0ms (31.4% of total)

ival-mult: 3.0ms (31.4% of total)

ival-sub: 1.0ms (10.5% of total)

ival-add: 1.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

series57.0ms (0.9%)

Memory

-23.5MiB live, 13.1MiB allocated

Counts

12 → 144

Calls

Call 1

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

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

Calls

36 calls:

Time	Variable		Point	Expression
51.0ms	x	@	-inf	(* (- 1 (* x x)) x)
0.0ms	x	@	0	(* (- 1 (* x x)) x)
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	inf	(* (- 1 (* x x)) x)
0.0ms	x	@	0	(/ 1 x)

simplify411.0ms (6.6%)

Memory

27.5MiB live, 301.1MiB allocated

Algorithm

1×	egg-herbie

Rules

16 526×	`lower-fma.f64`
16 526×	`lower-fma.f32`
3 386×	`lower-*.f64`
3 386×	`lower-*.f32`
1 774×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	1062
1	148	995
2	366	976
3	1174	956
4	4116	956
0	8075	889

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 138

Calls

Call 1

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

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

rewrite219.0ms (3.5%)

Memory

10.2MiB live, 309.3MiB allocated

Rules

3 986×	`lower-fma.f32`
3 984×	`lower-fma.f64`
3 868×	`lower-/.f32`
3 860×	`lower-/.f64`
3 160×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	84
0	25	83
1	82	83
2	426	81
3	4031	81
0	10245	81

Stop Event

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

Counts

12 → 945

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64)) (sqrt.f64 x))
(.f64 (/.f64 x (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
(*.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 x))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) x)
(.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 x (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (neg.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (neg.f64 (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))))) (neg.f64 (-.f64 (.f64 x (*.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 x))) #s(literal 1 binary64))
(/.f64 (neg.f64 (.f64 x (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))))) (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (-.f64 (.f64 x (.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))) (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 (fma.f64 x x #s(literal 1 binary64)) x))))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64)))) (neg.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (neg.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)))) (-.f64 (.f64 x (*.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))))) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 x x #s(literal 1 binary64)) x))))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64)))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (fma.f64 x x #s(literal -1 binary64)))
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(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) #s(approx (+ ( x x) 1) (*.f64 x x)))))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (+ (* x x) 1) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) #s(approx (+ (* x x) 1) (.f64 x x))) (/.f64 (neg.f64 x) #s(approx (+ ( x x) 1) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (+ (* x x) 1) (*.f64 x x))))
(exp.f64 (-.f64 (.f64 (log.f64 #s(approx (+ ( x x) 1) (*.f64 x x))) #s(literal -1 binary64)) (neg.f64 (log.f64 x))))
(exp.f64 (fma.f64 (log.f64 #s(approx (+ (* x x) 1) (*.f64 x x))) #s(literal -1 binary64) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log.f64 #s(approx (+ ( x x) 1) (*.f64 x x))) #s(literal -1 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (+ ( x x) 1) (*.f64 x x)) x)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (+ ( x x) 1) (*.f64 x x))))
(.f64 #s(approx (+ ( x x) 1) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (+ ( x x) 1) (*.f64 x x)))
(pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* x x) 1) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 #s(approx (+ (* x x) 1) (*.f64 x x)) #s(literal 1 binary64))
#s(approx (+ (* x x) 1) (*.f64 x x))
(/.f64 (neg.f64 #s(approx (+ (* x x) 1) (*.f64 x x))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx (+ (* x x) 1) (*.f64 x x))))
(/.f64 #s(approx (+ (* x x) 1) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ (* x x) 1) (*.f64 x x))))
(neg.f64 (neg.f64 #s(approx (+ (* x x) 1) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ (* x x) 1) (*.f64 x x))))
(exp.f64 (neg.f64 (.f64 (log.f64 #s(approx (+ ( x x) 1) (*.f64 x x))) #s(literal -1 binary64))))

eval443.0ms (7.1%)

Memory: 1.8MiB live, 294.6MiB allocated
Compiler: Compiled 30 714 to 1 904 computations (93.8% saved)

prune324.0ms (5.2%)

Memory

-2.1MiB live, 318.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1 115	1	1 116
Fresh	0	1	1
Picked	1	4	5
Done	0	0	0
Total	1 116	6	1 122

Accuracy

100.0%

Counts

1 122 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	28.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
▶	65.2%	(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
✓	51.2%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	50.4%	#s(approx (/ x (+ (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x))
▶	51.7%	#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))

Compiler

Compiled 50 to 25 computations (50% saved)

simplify285.0ms (4.6%)

Memory

3.2MiB live, 263.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))
cost-diff	0	(/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	1344	(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
cost-diff	0	#s(approx (- 1 (* x x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))

Rules

26 298×	`lower-fma.f32`
26 294×	`lower-fma.f64`
3 854×	`lower-*.f32`
3 848×	`lower-*.f64`
2 256×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
0	23	77
1	46	74
2	84	68
3	227	65
4	1101	63
5	4144	63
0	8462	61

Stop Event

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

Calls

Call 1

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

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

localize145.0ms (2.3%)

Memory

-15.2MiB live, 85.5MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0703125	(fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))
accuracy	3.0913626197782476	(/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))
accuracy	18.691830505862367	(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
accuracy	0.03125	(.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)
accuracy	31.74167271876838	#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))
accuracy	31.928580613893793	#s(approx (- 1 (* x x)) #s(literal 1 binary64))

Samples

75.0ms

256×

valid

Compiler

Compiled 70 to 15 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 6.0ms (41.7% of total)

ival-div: 3.0ms (20.9% of total)

ival-add: 3.0ms (20.9% of total)

ival-sub: 1.0ms (7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

8 → 96

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 3)) (taylor inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 3)) (taylor -inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt #s(approx (- 1 (* x x)) #s(literal 1 binary64)) (patch #s(approx (- 1 (* x x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -1 (pow x 4)) 1)) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 4) (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) 1)) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 3)) (taylor inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ 1 (pow x 4))) (pow x 3)) (taylor inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 3)) (taylor inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 3)) (taylor inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ 1 (pow x 4))) (pow x 3)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 4))) (pow x 4))) 1) (pow x 3))) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 4))) (pow x 8))) (+ 1 (/ 1 (pow x 4)))) (pow x 3))) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (patch (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 4) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 4) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 4) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1 (/ 1 (pow x 4)))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1 (/ 1 (pow x 4)))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1 (/ 1 (pow x 4)))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1 (/ 1 (pow x 4)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1 (/ 1 (pow x 4)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1 (/ 1 (pow x 4)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

24 calls:

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

simplify151.0ms (2.4%)

Memory

-3.6MiB live, 153.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 086×	`lower-fma.f64`
9 086×	`lower-fma.f32`
3 306×	`lower-*.f64`
3 306×	`lower-*.f32`
1 762×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	720
1	225	675
2	624	658
3	2094	637
4	6554	635
0	8216	626

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 93

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* -1 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 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))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* -1 x)
(* x (- (* -1 (pow x 4)) 1))
(* x (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1))
(* x (- (* (pow x 4) (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) 1))
(/ 1 (pow x 3))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 3))
(/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 3))
(/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 3))
(/ 1 (pow x 3))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 3))
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 4))) (pow x 4))) 1) (pow x 3)))
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 4))) (pow x 8))) (+ 1 (/ 1 (pow x 4)))) (pow x 3)))
-1
(- (pow x 4) 1)
(- (pow x 4) 1)
(- (pow x 4) 1)
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) (.f64 (.f64 x x) x)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) (.f64 (.f64 x x) x)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) x))
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* x (+ 1 (* -1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* x (+ 1 (* -1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* -1 (pow x 3))
(.f64 (neg.f64 x) (.f64 x x))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* -1 (pow x 3))
(.f64 (neg.f64 x) (.f64 x x))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) (.f64 (.f64 x x) x)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) (.f64 (.f64 x x) x)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) x))
-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))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (* -1 (pow x 4)) 1))
(.f64 (fma.f64 (neg.f64 x) (.f64 (*.f64 x x) x) #s(literal -1 binary64)) x)
(* x (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1))
(.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal 1 binary64)) (.f64 (neg.f64 x) (.f64 (.f64 x x) x)) #s(literal -1 binary64)) x)
(* x (- (* (pow x 4) (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) 1))
(.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) x)
(/ 1 (pow x 3))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 3))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (.f64 (*.f64 x x) x))
(/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 3))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x))) #s(literal 1 binary64)) (.f64 (.f64 x x) x))
(/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 3))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)))) (.f64 (.f64 x x) x))
(/ 1 (pow x 3))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 3))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (.f64 (*.f64 x x) x))
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 4))) (pow x 4))) 1) (pow x 3)))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (.f64 (.f64 x x) x))
(* -1 (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 4))) (pow x 8))) (+ 1 (/ 1 (pow x 4)))) (pow x 3)))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x))))) (.f64 (*.f64 x x) x))
-1
#s(literal -1 binary64)
(- (pow x 4) 1)
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(- (pow x 4) 1)
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(- (pow x 4) 1)
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(pow x 4)
(.f64 (.f64 (*.f64 x x) x) x)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(pow x 4)
(.f64 (.f64 (*.f64 x x) x) x)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite818.0ms (13.1%)

Memory

15.0MiB live, 324.7MiB allocated

Rules

8 610×	`lower-fma.f32`
8 606×	`lower-fma.f64`
4 686×	`lower-*.f32`
4 680×	`lower-*.f64`
4 152×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	73
0	23	70
1	99	59
2	734	59
0	8069	57

Stop Event

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

Counts

8 → 945

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))
(.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)
(.f64 x #s(approx (- 1 ( x x)) #s(literal 1 binary64)))
#s(approx (- 1 (* x x)) #s(literal 1 binary64))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) x) x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))) (fma.f64 (.f64 (.f64 x x) x) x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 x x)) x (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 x x)) (.f64 (.f64 x x) x) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 (.f64 x x) x) x)))))
(.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) x x) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 x x) x) (neg.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 (neg.f64 x) x) x x) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 x x)) x #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)))) (-.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 x x) #s(literal -1 binary64)))) (fma.f64 (.f64 (.f64 x x) x) (neg.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 x x)) x #s(literal -1 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 x (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (neg.f64 x) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 x x)) x #s(literal -1 binary64)))) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 x))
(*.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (/.f64 (neg.f64 x) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (neg.f64 x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 x x) #s(literal -1 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 x x) #s(literal -1 binary64))) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) x))
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(+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)))
(+.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(+.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (.f64 (.f64 (*.f64 x x) x) x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 (*.f64 x x) x) x))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 x (.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval359.0ms (5.8%)

Memory: 36.4MiB live, 287.7MiB allocated
Compiler: Compiled 34 872 to 2 761 computations (92.1% saved)

prune153.0ms (2.5%)

Memory

-19.9MiB live, 410.4MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	1 066	0	1 066
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	1 066	6	1 072

Accuracy

100.0%

Counts

1 072 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	28.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	65.2%	(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
✓	51.2%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	50.4%	#s(approx (/ x (+ (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x))
✓	51.7%	#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))

Compiler

Compiled 106 to 43 computations (59.4% saved)

regimes6.0ms (0.1%)

Memory

22.7MiB live, 22.7MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
99.9%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes3.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
100.0%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes19.0ms (0.3%)

Memory

-45.0MiB live, 16.5MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

16.0ms	x
2.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
80.2%	3	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.2%	2	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes2.0ms (0%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

12.9MiB live, 12.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
51.7%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
51.7%	1	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

bsearch10.0ms (0.2%)

Memory

0.3MiB live, 39.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
9.0ms	1211520.5845753176	62799374.31570225

Samples

5.0ms

112×

valid

Compiler

Compiled 172 to 93 computations (45.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (45.8% of total)

ival-mult: 1.0ms (45.8% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch3.0ms (0.1%)

Memory

-30.9MiB live, 8.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
3.0ms	62799374.31570225	607977118587.7227

Samples

1.0ms

32×

valid

Compiler

Compiled 39 to 27 computations (30.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch9.0ms (0.1%)

Memory

30.6MiB live, 30.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.04484387583172138	3.0528471201961787

Samples

4.0ms

112×

valid

Compiler

Compiled 123 to 79 computations (35.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (46.2% of total)

ival-add: 1.0ms (46.2% of total)

ival-mult: 1.0ms (46.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch4.0ms (0.1%)

Memory

-31.3MiB live, 8.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.04484387583172138	3.0528471201961787

Samples

2.0ms

32×

valid

Compiler

Compiled 102 to 65 computations (36.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult: 1.0ms (77.1% of total)

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

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

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

exact: 0.0ms (0% of total)

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

simplify6.0ms (0.1%)

Memory

20.1MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	130
1	44	130
2	50	130
3	54	130
4	56	130

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 60000000 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))

Outputs
(if (<=.f64 x #s(literal 60000000 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 60000000 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (- 1 ( x x)) #s(literal 1 binary64)) x))

soundness616.0ms (9.9%)

Memory

-7.8MiB live, 427.3MiB allocated

Rules

16 526×	`lower-fma.f64`
16 526×	`lower-fma.f32`
12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
4 942×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	1062
1	148	995
2	366	976
3	1174	956
4	4116	956
0	8075	889
0	45	226
1	131	224
2	312	216
3	888	212
4	2381	210
5	5550	210
6	7627	210
0	8047	197
0	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13

Stop Event

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

Compiler

Compiled 159 to 75 computations (52.8% saved)

preprocess113.0ms (1.8%)

Memory: 16.8MiB live, 172.7MiB allocated
Compiler: Compiled 224 to 94 computations (58% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6

start0.0ms (0%)

analyze0.0ms (0%)

sample526.0ms (8.4%)

explain268.0ms (4.3%)

preprocess24.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize20.0ms (0.3%)

series2.0ms (0%)

simplify193.0ms (3.1%)

rewrite165.0ms (2.7%)

eval127.0ms (2%)

prune260.0ms (4.2%)

simplify308.0ms (4.9%)

localize178.0ms (2.9%)

series57.0ms (0.9%)

simplify411.0ms (6.6%)

rewrite219.0ms (3.5%)

eval443.0ms (7.1%)

prune324.0ms (5.2%)

simplify285.0ms (4.6%)

localize145.0ms (2.3%)

series5.0ms (0.1%)

simplify151.0ms (2.4%)

rewrite818.0ms (13.1%)

eval359.0ms (5.8%)

prune153.0ms (2.5%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

regimes19.0ms (0.3%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch10.0ms (0.2%)

bsearch3.0ms (0.1%)

bsearch9.0ms (0.1%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

soundness616.0ms (9.9%)

preprocess113.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6