Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample971.0ms (14.6%)

Memory

26.7MiB live, 617.5MiB allocated

Samples

600.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-div: 117.0ms (51.1% of total)

ival-mult: 62.0ms (27.1% of total)

ival-add: 37.0ms (16.2% of total)

ival-true: 6.0ms (2.6% of total)

exact: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain90.0ms (1.3%)

Memory

-1.7MiB live, 95.8MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	64	0
-	0	192

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	192
1	64

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 46 to 19 computations (58.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (37.5% of total)

ival-div: 3.0ms (28.1% of total)

ival-add: 2.0ms (18.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess22.0ms (0.3%)

Memory

-22.7MiB live, 22.7MiB 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

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.7%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify4.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB 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)

localize19.0ms (0.3%)

Memory

-15.8MiB live, 29.1MiB 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	14.884859074536136	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

10.0ms

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 (41% of total)

ival-mult: 2.0ms (41% of total)

ival-add: 1.0ms (20.5% 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

4.5MiB live, 4.5MiB 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))

simplify286.0ms (4.3%)

Memory

3.2MiB live, 293.2MiB 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))))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x x #s(literal -1 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))))
(/ 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 (/.f64 #s(literal 1 binary64) (.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 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 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 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.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 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 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)

rewrite438.0ms (6.6%)

Memory

13.1MiB live, 391.7MiB 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 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x (neg.f64 x))))
(+.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(+.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(-.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
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eval70.0ms (1%)

Memory: -13.3MiB live, 76.1MiB allocated
Compiler: Compiled 12 336 to 1 050 computations (91.5% saved)

prune95.0ms (1.4%)

Memory

9.0MiB live, 122.0MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	355	7	362
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	356	7	363

Accuracy

100.0%

Counts

363 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.6%	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))
▶	76.7%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	24.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
▶	54.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
	76.7%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
▶	53.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
▶	47.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 116 to 60 computations (48.3% saved)

simplify582.0ms (8.7%)

Memory

-9.1MiB live, 358.7MiB 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	(neg.f64 x)
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) (neg.f64 x) x)
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 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

15 632×	`lower-fma.f32`
15 628×	`lower-fma.f64`
3 620×	`lower-+.f64`
3 620×	`lower-+.f32`
3 270×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	92
0	26	92
1	38	92
2	53	88
3	77	88
4	97	88
5	155	88
6	226	88
7	472	88
8	985	88
9	1747	88
10	3109	88
11	3959	88
12	5293	88
13	5762	88
14	5906	88
15	5934	88
16	5970	88
17	5994	88
18	6222	88
19	6276	88
20	6276	88
0	8188	88

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)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(*.f64 x x)
x
(neg.f64 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)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 x (.f64 x x))))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(-.f64 x (.f64 x (.f64 x x)))
(*.f64 x x)
x
(neg.f64 x)
(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
x
#s(approx (+ (* x x) 1) (*.f64 x x))
(*.f64 x x)

localize39.0ms (0.6%)

Memory

18.8MiB live, 104.3MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	14.884859074536136	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
accuracy	33.24806219028425	#s(approx (+ (* x x) 1) (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0	(neg.f64 x)
accuracy	0.03125	(fma.f64 (*.f64 x x) (neg.f64 x) x)
accuracy	29.639679118271427	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
accuracy	14.884859074536136	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	28.977138206692313	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	33.3807197568424	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	14.884859074536136	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

20.0ms

256×

valid

Compiler

Compiled 79 to 11 computations (86.1% saved)

Precisions

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

ival-div: 3.0ms (28.9% of total)

ival-mult: 3.0ms (28.9% of total)

ival-add: 2.0ms (19.3% of total)

ival-neg: 1.0ms (9.6% 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

16.3MiB live, 16.3MiB 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)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 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>) () ())) ())
#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(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 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) 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 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)) 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)) (+ 1 (/ 1 (pow x 4)))) 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)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) 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 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#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 (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#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 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 x) (#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 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 x) (#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 (/ 1 x) (taylor inf x) (#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 (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#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 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x) (taylor inf x) (#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 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x) (taylor inf x) (#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 (/ 1 x) (taylor -inf x) (#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 (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#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 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x)) (taylor -inf x) (#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 (* -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) #s(literal 1 binary64))) (patch (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#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 (+ 1 (pow x 2)) (taylor 0 x) (#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 (+ 1 (pow x 2)) (taylor 0 x) (#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 (+ 1 (pow x 2)) (taylor 0 x) (#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 (pow x 2) (taylor inf x) (#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 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#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 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#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 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#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 (pow x 2) (taylor -inf x) (#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 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#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 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#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 (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#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 x (taylor 0 x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) 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)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) 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)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow x 2))) x) (taylor inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) 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)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) 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)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) 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)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.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 #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) (patch #s(approx (/ x (+ ( x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (neg.f64 x) x) (patch (fma.f64 (.f64 x x) (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 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 (* x (+ 1 (* -1 (pow x 2)))) (taylor 0 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 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1)))) (taylor 0 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 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))) (taylor 0 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 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))) 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 4))) (/ 1 (pow x 2))) 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 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) 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 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
0.0ms	x	@	0	(+ (* (* x x) (neg x)) x)
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	inf	(+ (* (* x x) (neg x)) x)
0.0ms	x	@	0	(/ 1 x)
0.0ms	x	@	-inf	(+ (* (* x x) (neg x)) x)

simplify476.0ms (7.1%)

Memory

-11.6MiB live, 461.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 496×	`lower-fma.f64`
16 496×	`lower-fma.f32`
3 370×	`lower-*.f64`
3 370×	`lower-*.f32`
1 780×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	1023
1	149	965
2	361	946
3	1167	926
4	4167	926
0	8145	859

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)))))
(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)
(* -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))))

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

rewrite275.0ms (4.1%)

Memory

45.2MiB live, 279.6MiB allocated

Rules

3 888×	`lower-fma.f32`
3 884×	`lower-fma.f64`
2 316×	`lower-*.f32`
2 314×	`lower-*.f64`
1 842×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	81
0	26	81
1	88	77
2	505	77
3	4376	76
0	9009	76

Stop Event

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

Counts

12 → 490

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)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(*.f64 x x)
(neg.f64 x)
(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
#s(approx (+ (* x x) 1) (*.f64 x x))

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

eval77.0ms (1.2%)

Memory: -20.6MiB live, 165.8MiB allocated
Compiler: Compiled 11 100 to 1 057 computations (90.5% saved)

prune112.0ms (1.7%)

Memory

31.3MiB live, 123.6MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	672	1	673
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	673	7	680

Accuracy

100.0%

Counts

680 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.4%	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	76.7%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	24.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	54.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	76.7%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
✓	53.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
✓	47.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 53 to 26 computations (50.9% saved)

simplify522.0ms (7.8%)

Memory

-7.9MiB live, 384.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x (*.f64 x x) x)
cost-diff	0	(*.f64 x x)
cost-diff	640	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	192	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
cost-diff	512	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))

Rules

14 660×	`lower-fma.f32`
14 656×	`lower-fma.f64`
6 306×	`lower-*.f32`
6 304×	`lower-*.f64`
2 748×	`cube-prod`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	8	40
0	15	37
1	26	37
2	31	33
3	41	33
4	105	33
5	233	33
6	759	32
7	2017	32
8	2538	32
9	3270	32
10	3782	32
11	4396	32
12	5189	32
13	5561	32
14	5796	32
15	7452	32
16	7621	32
17	7797	32
0	8426	32

Stop Event

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

Calls

Call 1

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

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

localize177.0ms (2.7%)

Memory

-11.2MiB live, 46.7MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.03125	(fma.f64 x (*.f64 x x) x)
accuracy	35.27876679337926	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0.08984375	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
accuracy	14.879190564792799	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)

Samples

16.0ms

256×

valid

Compiler

Compiled 47 to 11 computations (76.6% saved)

Precisions

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

ival-div: 4.0ms (40.2% of total)

ival-mult: 3.0ms (30.1% of total)

ival-add: 2.0ms (20.1% of total)

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

exact: 0.0ms (0% of total)

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

series48.0ms (0.7%)

Memory

-35.9MiB live, 6.1MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

18 calls:

Time	Variable		Point	Expression
45.0ms	x	@	-inf	(/ (+ (* x x) 1) x)
0.0ms	x	@	0	(/ (+ (* x x) 1) x)
0.0ms	x	@	inf	(/ (+ (* x x) 1) x)
0.0ms	x	@	inf	(/ (* x x) (+ (* x (* x x)) x))
0.0ms	x	@	0	(/ (* x x) (+ (* x (* x x)) x))

simplify355.0ms (5.3%)

Memory

35.2MiB live, 506.2MiB allocated

Algorithm

1×	egg-herbie

Rules

19 038×	`lower-fma.f64`
19 038×	`lower-fma.f32`
4 046×	`lower-*.f64`
4 046×	`lower-*.f32`
1 846×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	502
1	154	468
2	344	464
3	1486	438
4	6421	438
0	8566	417

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 67

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 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
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)
x
(* x (+ 1 (pow x 2)))
(* x (+ 1 (pow x 2)))
(* x (+ 1 (pow x 2)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))

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

rewrite230.0ms (3.4%)

Memory

22.0MiB live, 437.2MiB allocated

Rules

4 834×	`lower-fma.f32`
4 830×	`lower-fma.f64`
3 334×	`lower-*.f32`
3 332×	`lower-*.f64`
2 370×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	37
0	15	34
1	72	30
2	460	30
3	4458	29
0	8285	29

Stop Event

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

Counts

6 → 747

Calls

Call 1

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

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

eval293.0ms (4.4%)

Memory: 10.1MiB live, 225.2MiB allocated
Compiler: Compiled 21 341 to 1 739 computations (91.9% saved)

prune128.0ms (1.9%)

Memory

1.3MiB live, 327.9MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	843	1	844
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	844	7	851

Accuracy

100.0%

Counts

851 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	44.4%	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	76.7%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	24.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	54.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
✓	53.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
✓	47.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 52 to 26 computations (50% saved)

simplify4.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.3%)

Memory

-5.3MiB live, 42.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(+.f64 (/.f64 #s(literal 1 binary64) x) x)
accuracy	0.08984375	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))

Samples

12.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 5.0ms (73.9% of total)

ival-add: 1.0ms (14.8% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

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

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

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

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

Calls

9 calls:

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

simplify199.0ms (3%)

Memory

28.7MiB live, 307.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 656×	`lower-fma.f64`
12 656×	`lower-fma.f32`
3 048×	`lower-*.f64`
3 048×	`lower-*.f32`
1 642×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	254
1	132	240
2	309	232
3	874	216
4	2378	214
5	5529	214
6	7683	214
0	8117	207

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 33

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

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

rewrite163.0ms (2.4%)

Memory

-47.0MiB live, 130.5MiB allocated

Rules

1 416×	`lower-fma.f64`
1 416×	`lower-fma.f32`
1 234×	`lower-*.f64`
1 234×	`lower-*.f32`
1 082×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	38	15
2	258	15
0	2449	15

Stop Event

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

Counts

3 → 180

Calls

Call 1

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

Outputs
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x))) (neg.f64 x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)))) (.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x))) (/.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x))))
(-.f64 (/.f64 (fma.f64 x x (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x))) (.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
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(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (fma.f64 x x (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 x) (/.f64 #s(literal -1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 x)))
(/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x x))) (neg.f64 x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (/.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) (fma.f64 (/.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) (/.f64 (*.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x)))) (.f64 (/.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (.f64 x x))) (/.f64 (*.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) x) x))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 (.f64 (neg.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (.f64 (+.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x)) #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal -1 binary64) x) x))
(/.f64 (.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x))) (fma.f64 x x (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)))) (-.f64 (/.f64 #s(literal 1 binary64) x) x))
(pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x))))
(*.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x))
(*.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) #s(literal 1 binary64)))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) #s(literal 1 binary64)))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))))
(.f64 (+.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)))
(.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (neg.f64 (log.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))

eval22.0ms (0.3%)

Memory: 9.1MiB live, 54.6MiB allocated
Compiler: Compiled 4 742 to 508 computations (89.3% saved)

prune37.0ms (0.6%)

Memory

-4.2MiB live, 91.9MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	213	7	220

Accuracy

100.0%

Counts

220 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	44.4%	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	76.7%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	24.5%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	54.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
✓	53.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
✓	47.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 128 to 50 computations (60.9% saved)

regimes10.0ms (0.2%)

Memory

-25.0MiB live, 20.6MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 10 to 6 computations (40% saved)

regimes5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#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)) (fma.f64 (*.f64 x x) (neg.f64 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

2 calls:

3.0ms	x
2.0ms	(/.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)

regimes4.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#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)) (fma.f64 (*.f64 x x) (neg.f64 x) x))
(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
78.9%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
98.7%	2	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes2.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
98.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

7.7MiB live, 7.7MiB 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(literal 1 binary64) x))

Outputs
#s(approx (/ x (+ (* x x) 1)) (/.f64 #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
47.8%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
47.8%	1	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

bsearch2.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	87851.50626743946	349114405536.0351

Samples

1.0ms

16×

valid

Compiler

Compiled 25 to 18 computations (28% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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)

bsearch11.0ms (0.2%)

Memory

-26.8MiB live, 19.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.06135963893478422	220.33312415057992

Samples

6.0ms

128×

valid

Compiler

Compiled 139 to 81 computations (41.7% saved)

Precisions

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

ival-div: 1.0ms (40.7% of total)

ival-add: 1.0ms (40.7% of total)

ival-mult: 1.0ms (40.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch3.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.06135963893478422	220.33312415057992

Samples

1.0ms

32×

valid

Compiler

Compiled 107 to 73 computations (31.8% 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)

simplify6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	93
1	32	93
2	34	93
3	35	93

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
(if (<=.f64 x #s(literal 100000 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 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 100000 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 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 x x) (neg.f64 x) x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

soundness720.0ms (10.8%)

Memory

6.9MiB live, 429.2MiB allocated

Rules

12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
4 942×	`lower-/.f32`
4 940×	`lower-/.f64`
4 834×	`lower-fma.f32`

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
0	8	37
0	15	34
1	72	30
2	460	30
3	4458	29
0	8285	29
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×	iter limit
1×	node limit

Compiler

Compiled 137 to 63 computations (54% saved)

preprocess147.0ms (2.2%)

Memory: 14.8MiB live, 206.4MiB allocated
Compiler: Compiled 200 to 90 computations (55% 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%)

sample971.0ms (14.6%)

explain90.0ms (1.3%)

preprocess22.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize19.0ms (0.3%)

series2.0ms (0%)

simplify286.0ms (4.3%)

rewrite438.0ms (6.6%)

eval70.0ms (1%)

prune95.0ms (1.4%)

simplify582.0ms (8.7%)

localize39.0ms (0.6%)

series5.0ms (0.1%)

simplify476.0ms (7.1%)

rewrite275.0ms (4.1%)

eval77.0ms (1.2%)

prune112.0ms (1.7%)

simplify522.0ms (7.8%)

localize177.0ms (2.7%)

series48.0ms (0.7%)

simplify355.0ms (5.3%)

rewrite230.0ms (3.4%)

eval293.0ms (4.4%)

prune128.0ms (1.9%)

simplify4.0ms (0.1%)

localize17.0ms (0.3%)

series1.0ms (0%)

simplify199.0ms (3%)

rewrite163.0ms (2.4%)

eval22.0ms (0.3%)

prune37.0ms (0.6%)

regimes10.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch2.0ms (0%)

bsearch11.0ms (0.2%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

soundness720.0ms (10.8%)

preprocess147.0ms (2.2%)

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