Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample953.0ms (19.7%)

Memory

30.3MiB live, 642.0MiB allocated

Samples

751.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 298.0ms

ival-mult: 190.0ms (63.7% of total)

ival-div: 55.0ms (18.4% of total)

ival-add: 39.0ms (13.1% of total)

ival-true: 6.0ms (2% of total)

exact: 5.0ms (1.7% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

explain72.0ms (1.5%)

Memory

1.2MiB live, 84.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
54	-	-	`(/.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	54	0
↳	`(*.f64 x x)`	overflow	54
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	54

Confusion

	Predicted +	Predicted -
+	54	0
-	0	202

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	54	0	0
-	0	0	202

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	202
1	54

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 62 to 27 computations (56.5% saved)

Precisions

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

ival-mult: 4.0ms (36.7% of total)

ival-div: 3.0ms (27.5% of total)

ival-add: 2.0ms (18.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess24.0ms (0.5%)

Memory

-3.8MiB live, 31.7MiB 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 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	80.2%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB 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)

localize17.0ms (0.3%)

Memory

-10.7MiB live, 27.0MiB 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	12.643224200689428	(/.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 (38.8% of total)

ival-mult: 2.0ms (38.8% of total)

ival-add: 1.0ms (19.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB 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 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 (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 (.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 (/ 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 (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 (.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 (/ 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 -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify153.0ms (3.2%)

Memory

16.2MiB live, 173.8MiB 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	883	212
4	2385	210
5	5560	210
6	7661	210
0	8081	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))
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))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 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)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 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)

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))
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (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 (pow.f64 x #s(literal 5 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(/ 1 x)
(/.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 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) 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 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(/ 1 x)
(/.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 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) 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 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite233.0ms (4.8%)

Memory

24.9MiB live, 212.8MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 327

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal -1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(fma.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 x x) (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(fma.f64 (.f64 x x) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64))) (/.f64 (/.f64 (*.f64 x x) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x x) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (*.f64 #s(literal -1 binary64) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 x x)) (*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))))
(+.f64 (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval78.0ms (1.6%)

Memory: -33.9MiB live, 95.4MiB allocated
Compiler: Compiled 7 796 to 1 076 computations (86.2% saved)

prune251.0ms (5.2%)

Memory

-13.6MiB live, 74.6MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	358	4	362
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	359	4	363

Accuracy

100.0%

Counts

363 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.7%	(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
▶	80.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	49.3%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 26 to 21 computations (19.2% saved)

simplify155.0ms (3.2%)

Memory

27.1MiB live, 179.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f64 x #s(literal 4 binary64))
cost-diff	0	(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	0	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
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))

Rules

13 064×	`lower-fma.f32`
13 060×	`lower-fma.f64`
2 620×	`lower-*.f32`
2 618×	`lower-*.f64`
2 014×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	77
0	27	77
1	39	77
2	60	77
3	119	75
4	261	75
5	684	75
6	1509	75
7	3378	75
8	5332	75
9	7568	75
0	8046	75

Stop Event

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

Calls

Call 1

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

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

localize40.0ms (0.8%)

Memory

13.6MiB live, 86.2MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 4 binary64))
accuracy	0	(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))
accuracy	0.05078125	(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
accuracy	21.548256752638675	(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	12.643224200689428	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
accuracy	12.643224200689428	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	30.08120235686192	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	32.43211569613511	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Samples

30.0ms

256×

valid

Compiler

Compiled 79 to 15 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 7.0ms (40.4% of total)

ival-mult: 4.0ms (23.1% of total)

ival-pow: 3.0ms (17.3% of total)

ival-add: 2.0ms (11.5% of total)

ival-sub: 1.0ms (5.8% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

-20.1MiB live, 18.0MiB allocated

Counts

11 → 132

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

simplify158.0ms (3.3%)

Memory

22.6MiB live, 231.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 858×	`lower-fma.f64`
12 858×	`lower-fma.f32`
3 446×	`lower-*.f64`
3 446×	`lower-*.f32`
1 768×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	903
1	158	862
2	382	845
3	1136	829
4	4414	829
0	8206	770

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 128

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

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

rewrite172.0ms (3.6%)

Memory

19.0MiB live, 270.9MiB allocated

Rules

4 726×	`lower-fma.f32`
4 722×	`lower-fma.f64`
4 388×	`lower-*.f32`
4 386×	`lower-*.f64`
4 182×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	67
0	27	61
1	106	61
2	601	60
0	8260	60

Stop Event

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

Counts

11 → 1 266

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) (pow.f64 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)))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) x) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) #s(approx (+ ( x x) 1) #s(literal 1 binary64))) (neg.f64 x))
(.f64 (pow.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)) #s(literal -1 binary64)) x)
(.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (+ ( x x) 1) #s(literal 1 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) #s(approx (+ ( x x) 1) #s(literal 1 binary64))))
(.f64 (/.f64 x #s(approx (+ ( x x) 1) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 x #s(approx (+ ( x x) 1) #s(literal 1 binary64))))
(.f64 x (pow.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) x) #s(literal -1 binary64))
(/.f64 (.f64 (pow.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64))))
(/.f64 (/.f64 (neg.f64 x) #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (.f64 (neg.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 x) (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64))) x))
(/.f64 (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) x))
(/.f64 x (.f64 (neg.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64))) #s(literal -1 binary64)))
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) x)))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) #s(approx (+ ( x x) 1) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)))) (/.f64 (neg.f64 x) #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64))))
(.f64 #s(approx (+ ( x x) 1) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (+ ( x x) 1) #s(literal 1 binary64)))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ (* x x) 1) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (neg.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (neg.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 x (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 x x x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)))) (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x x) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 x (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 x (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (/.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) x (-.f64 x (pow.f64 x #s(literal 3 binary64)))))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
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eval259.0ms (5.3%)

Memory: -16.2MiB live, 362.0MiB allocated
Compiler: Compiled 29 943 to 2 924 computations (90.2% saved)

prune218.0ms (4.5%)

Memory

-8.8MiB live, 259.1MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1 393	1	1 394
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	1 394	4	1 398

Accuracy

100.0%

Counts

1 398 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.7%	(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 (.f64 (*.f64 (neg.f64 x) x) x) (neg.f64 x) #s(literal -1 binary64)))
✓	80.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	49.3%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify232.0ms (4.8%)

Memory

24.0MiB live, 219.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	448	(fma.f64 (.f64 (.f64 (neg.f64 x) x) x) (neg.f64 x) #s(literal -1 binary64))
cost-diff	12928	(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 (.f64 (*.f64 (neg.f64 x) x) x) (neg.f64 x) #s(literal -1 binary64)))

Rules

17 172×	`lower-fma.f32`
17 168×	`lower-fma.f64`
3 126×	`lower-*.f32`
3 120×	`lower-*.f64`
1 544×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	51
0	18	51
1	39	49
2	98	41
3	277	37
4	722	33
5	3174	33
0	8532	32

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.7%)

Memory

-4.8MiB live, 67.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
accuracy	0.0546875	(fma.f64 (.f64 (.f64 (neg.f64 x) x) x) (neg.f64 x) #s(literal -1 binary64))
accuracy	0.07421875	(.f64 (.f64 (neg.f64 x) x) x)
accuracy	21.548256752638675	(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 (.f64 (*.f64 (neg.f64 x) x) x) (neg.f64 x) #s(literal -1 binary64)))

Samples

25.0ms

256×

valid

Compiler

Compiled 58 to 13 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 8.0ms (59.6% of total)

ival-div: 2.0ms (14.9% of total)

ival-add: 2.0ms (14.9% of total)

ival-neg: 1.0ms (7.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify116.0ms (2.4%)

Memory

-17.1MiB live, 115.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 770×	`lower-fma.f64`
8 770×	`lower-fma.f32`
2 238×	`lower-*.f64`
2 238×	`lower-*.f32`
1 568×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	409
1	150	392
2	363	381
3	1123	377
4	3364	377
5	7846	377
0	8049	368

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 71

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

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

rewrite123.0ms (2.5%)

Memory

3.1MiB live, 228.0MiB allocated

Rules

3 256×	`lower-fma.f32`
3 252×	`lower-fma.f64`
2 674×	`lower-*.f32`
2 668×	`lower-*.f64`
2 118×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	47
0	18	47
1	71	34
2	479	26
3	6651	26
0	8073	26

Stop Event

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

Counts

6 → 636

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 x x #s(literal -1 binary64)))) (expm1.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 7 binary64)) x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 7 binary64)) x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 x (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 x (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (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 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (fma.f64 x x x) #s(literal -1 binary64)) (/.f64 (-.f64 x #s(literal 1 binary64)) (expm1.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64))))
(*.f64 (/.f64 (fma.f64 x x x) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (/.f64 x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) (/.f64 x (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
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(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 7 binary64)) x)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal 5 binary64)) x)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal 7 binary64)) x)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 7 binary64)) x) #s(literal 1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) x) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64))) x)
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 x x) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (.f64 (*.f64 x x) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (expm1.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (*.f64 x (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 x x) (expm1.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x)
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 x x)) (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) x))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (*.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (.f64 x x)) (*.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) x))
(/.f64 (.f64 (expm1.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (pow.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)))
(/.f64 (.f64 (expm1.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) x) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) x) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 7 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 7 binary64)) x) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 5 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 7 binary64)) x)))
(/.f64 (.f64 x x) (.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(/.f64 (*.f64 x x) (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(/.f64 x (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (fma.f64 x x x) x (*.f64 (fma.f64 x x x) #s(literal -1 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal -2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) x)
(fma.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (*.f64 x x) (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (*.f64 x x) x x)
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 0 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 #s(literal -1 binary64) x (pow.f64 x #s(literal 3 binary64)))
(fma.f64 x (fma.f64 x x x) (*.f64 #s(literal -1 binary64) (fma.f64 x x x)))
(fma.f64 x #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 x (*.f64 x x) x)
(fma.f64 x #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))
(-.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 0 binary64)) x)
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(+.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 0 binary64)) x)
(+.f64 (.f64 x (fma.f64 x x x)) (.f64 #s(literal -1 binary64) (fma.f64 x x x)))
(+.f64 (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(+.f64 (.f64 (fma.f64 x x x) x) (.f64 (fma.f64 x x x) #s(literal -1 binary64)))
(+.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 0 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(+.f64 (pow.f64 x #s(literal 3 binary64)) x)
(+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(+.f64 x (pow.f64 x #s(literal 3 binary64)))

eval103.0ms (2.1%)

Memory: 34.4MiB live, 184.6MiB allocated
Compiler: Compiled 15 056 to 1 807 computations (88% saved)

prune128.0ms (2.6%)

Memory

-22.2MiB live, 223.6MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	706	1	707
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	707	4	711

Accuracy

100.0%

Counts

711 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	80.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	99.8%	(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
✓	49.3%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify8.0ms (0.2%)

Memory

15.3MiB live, 15.3MiB 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 x (/.f64 #s(literal -1 binary64) x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 #s(literal -1 binary64) x)))

Rules

96×	`lower-fma.f64`
96×	`lower-fma.f32`
64×	`lower-*.f64`
64×	`lower-*.f32`
40×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	13	18
2	20	18
3	29	18
4	40	18
5	62	18
6	90	18
7	131	18
8	145	18
9	166	18
10	178	18
0	178	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.4%)

Memory

0.1MiB live, 39.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal -1 binary64) x)
accuracy	0.0078125	(-.f64 x (/.f64 #s(literal -1 binary64) x))
accuracy	0.10546875	(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 #s(literal -1 binary64) x)))

Samples

13.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-div: 5.0ms (76.2% of total)

ival-sub: 1.0ms (15.2% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

-33.8MiB live, 5.1MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

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

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

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

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((/ 1 (- x (/ -1 x))) (- x (/ -1 x)) (/ -1 x))
0.0ms	x	@	0	((/ 1 (- x (/ -1 x))) (- x (/ -1 x)) (/ -1 x))
0.0ms	x	@	-inf	((/ 1 (- x (/ -1 x))) (- x (/ -1 x)) (/ -1 x))

simplify150.0ms (3.1%)

Memory

31.2MiB live, 185.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 656×	`lower-fma.f64`
12 656×	`lower-fma.f32`
3 050×	`lower-*.f64`
3 050×	`lower-*.f32`
1 642×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	254
1	133	240
2	310	232
3	870	216
4	2379	214
5	5529	214
6	7671	214
0	8106	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 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ 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)
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 (/ (- (/ 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 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)

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

rewrite92.0ms (1.9%)

Memory

-13.5MiB live, 104.8MiB allocated

Rules

1 284×	`frac-times`
1 124×	`lower-*.f64`
1 124×	`lower-*.f32`
1 028×	`lower-/.f32`
1 024×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	40	15
2	280	15
0	3948	15

Stop Event

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

Counts

3 → 186

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)))) (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (/.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 9 binary64)))) (+.f64 (+.f64 (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (fma.f64 #s(literal -1 binary64) x (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)))) (fma.f64 x x (pow.f64 x #s(literal -2 binary64))))
(*.f64 (/.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)))) (+.f64 (+.f64 (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64)))) (fma.f64 #s(literal -1 binary64) x (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))
(.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) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (pow.f64 (pow.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (-.f64 x (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(.f64 (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (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 x (pow.f64 x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))))
(*.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) (-.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(/.f64 (/.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (/.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) (-.f64 x (pow.f64 x #s(literal -1 binary64)))) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64)))) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (-.f64 (.f64 x x) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (-.f64 (*.f64 x x) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal -2 binary64))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64)))) (.f64 (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64))) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (pow.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (-.f64 (.f64 x x) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)))))
(/.f64 (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 #s(literal -1 binary64) x (pow.f64 x #s(literal -1 binary64))) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64))))
(/.f64 (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) (-.f64 (*.f64 x x) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64))) (.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal -2 binary64))) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(/.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)))
(neg.f64 (pow.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) x) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) x))
(fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) x (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 x x (pow.f64 x #s(literal -2 binary64))) (*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 x x)))
(fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 x x) (.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal -2 binary64))) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))))
(fma.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (.f64 x x) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))))
(fma.f64 (.f64 x x) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (*.f64 x (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64))))))
(fma.f64 x (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64)))) (*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal -2 binary64))))))
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(/.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal -2 binary64))) (neg.f64 (fma.f64 #s(literal -1 binary64) x (pow.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal -2 binary64))) (-.f64 x (pow.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64))
(/.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)))
(neg.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (-.f64 (*.f64 x x) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64))))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x x) (pow.f64 x #s(literal -2 binary64)))) (-.f64 x (/.f64 #s(literal -1 binary64) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64))))))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64) x)
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x) x)
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(fma.f64 x (/.f64 x (-.f64 x (pow.f64 x #s(literal -1 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64))))))
(fma.f64 x #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (pow.f64 x #s(literal -1 binary64)))
(-.f64 (+.f64 x #s(literal 0 binary64)) (/.f64 #s(literal -1 binary64) x))
(-.f64 (/.f64 (*.f64 x (/.f64 x (-.f64 x (pow.f64 x #s(literal -1 binary64))))) #s(literal 1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x (pow.f64 x #s(literal -1 binary64))))) (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x))
(-.f64 x (/.f64 #s(literal -1 binary64) x))
(exp.f64 (neg.f64 (*.f64 (log.f64 (-.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x (pow.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 x (pow.f64 x #s(literal -1 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))))
(+.f64 (pow.f64 x #s(literal -1 binary64)) x)
(+.f64 x (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (neg.f64 x) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) x)
(/.f64 #s(literal 1 binary64) (neg.f64 x))
(neg.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(neg.f64 (pow.f64 x #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal -1 binary64)))

eval27.0ms (0.6%)

Memory: -3.8MiB live, 33.0MiB allocated
Compiler: Compiled 4 232 to 555 computations (86.9% saved)

prune46.0ms (0.9%)

Memory

-5.6MiB live, 40.7MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	219	4	223

Accuracy

100.0%

Counts

223 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	80.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	99.8%	(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
✓	49.3%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 78 to 44 computations (43.6% saved)

regimes6.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

7 → 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)))
(/.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 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 (.f64 (*.f64 (neg.f64 x) x) x) (neg.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB 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)))
(/.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:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB 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

2 calls:

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

Results

Accuracy	Segments	Branch
76.8%	4	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
98.1%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

-29.9MiB live, 7.2MiB 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:

3.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
49.3%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
49.3%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	27924177.005779162	734503417.2887713

Samples

1.0ms

16×

valid

Compiler

Compiled 20 to 19 computations (5% 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

18.6MiB live, 18.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.0002051819641989123	4.303534036334453

Samples

5.0ms

128×

valid

Compiler

Compiled 74 to 89 computations (-20.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (39.2% of total)

ival-add: 1.0ms (39.2% of total)

ival-mult: 1.0ms (39.2% of total)

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.5%)

Memory

11.0MiB live, 47.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative-binary64-+.f64`
8×	`sub-neg-binary64-neg.f64-+.f64--.f64`
6×	`neg-sub0-binary64--.f64-neg.f64`
6×	`neg-mul-1-binary64-*.f64-neg.f64`
4×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	63
1	25	63
2	32	63
3	38	63
4	42	63
5	44	63

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
(if (<=.f64 x #s(literal 50000000 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 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 x (/.f64 #s(literal -1 binary64) x)))
(if (<=.f64 x #s(literal 50000000 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 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))

soundness731.0ms (15.1%)

Memory

-2.1MiB live, 500.7MiB allocated

Rules

12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
4 942×	`lower-/.f32`
4 940×	`lower-/.f64`
4 762×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	226
1	131	224
2	312	216
3	883	212
4	2385	210
5	5560	210
6	7661	210
0	8081	197
0	9	47
0	18	47
1	71	34
2	479	26
3	6651	26
0	8073	26
0	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13
0	18	67
0	27	61
1	106	61
2	601	60
0	8260	60

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

Compiler

Compiled 127 to 71 computations (44.1% saved)

preprocess174.0ms (3.6%)

Memory: 22.3MiB live, 264.8MiB allocated
Compiler: Compiled 130 to 72 computations (44.6% 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	6	18
0	9	18
1	13	18
2	20	18
3	29	18
4	40	18
5	62	18
6	90	18
7	131	18
8	145	18
9	166	18
10	178	18
0	178	18

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	6	18
0	9	18
1	13	18
2	20	18
3	29	18
4	40	18
5	62	18
6	90	18
7	131	18
8	145	18
9	166	18
10	178	18
0	178	18

start0.0ms (0%)

analyze0.0ms (0%)

sample953.0ms (19.7%)

explain72.0ms (1.5%)

preprocess24.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize17.0ms (0.3%)

series3.0ms (0.1%)

simplify153.0ms (3.2%)

rewrite233.0ms (4.8%)

eval78.0ms (1.6%)

prune251.0ms (5.2%)

simplify155.0ms (3.2%)

localize40.0ms (0.8%)

series9.0ms (0.2%)

simplify158.0ms (3.3%)

rewrite172.0ms (3.6%)

eval259.0ms (5.3%)

prune218.0ms (4.5%)

simplify232.0ms (4.8%)

localize32.0ms (0.7%)

series6.0ms (0.1%)

simplify116.0ms (2.4%)

rewrite123.0ms (2.5%)

eval103.0ms (2.1%)

prune128.0ms (2.6%)

simplify8.0ms (0.2%)

localize18.0ms (0.4%)

series4.0ms (0.1%)

simplify150.0ms (3.1%)

rewrite92.0ms (1.9%)

eval27.0ms (0.6%)

prune46.0ms (0.9%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch2.0ms (0%)

bsearch11.0ms (0.2%)

simplify25.0ms (0.5%)

soundness731.0ms (15.1%)

preprocess174.0ms (3.6%)

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

Iter	Nodes	Cost
0	6	18
0	9	18
1	13	18
2	20	18
3	29	18
4	40	18
5	62	18
6	90	18
7	131	18
8	145	18
9	166	18
10	178	18
0	178	18