Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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)

sample609.0ms (12.9%)

Memory

13.2MiB live, 659.3MiB allocated

Samples

347.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 203.0ms

ival-div: 83.0ms (41% of total)

ival-mult: 62.0ms (30.6% of total)

ival-add: 43.0ms (21.2% of total)

ival-true: 6.0ms (3% of total)

exact: 6.0ms (3% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain185.0ms (3.9%)

Memory

-8.1MiB live, 70.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
71	-	-	`(/.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	71	0
↳	`(*.f64 x x)`	overflow	71
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	71

Confusion

	Predicted +	Predicted -
+	71	0
-	0	185

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	71	0	0
-	0	0	185

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	185
1	71

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

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

ival-mult: 4.0ms (37.4% of total)

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

ival-add: 2.0ms (18.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess20.0ms (0.4%)

Memory

32.4MiB live, 32.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.0%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify9.0ms (0.2%)

Memory

-31.0MiB live, 4.6MiB 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)

localize15.0ms (0.3%)

Memory

27.0MiB 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	16.646492131228946	(/.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 (40.1% of total)

ival-mult: 2.0ms (40.1% of total)

ival-add: 1.0ms (20% 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

4.9MiB live, 4.9MiB 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))

simplify177.0ms (3.8%)

Memory

-0.4MiB live, 117.0MiB 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)

rewrite181.0ms (3.8%)

Memory

7.9MiB live, 245.4MiB 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
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eval43.0ms (0.9%)

Memory: -2.6MiB live, 72.4MiB allocated
Compiler: Compiled 7 796 to 1 076 computations (86.2% saved)

prune31.0ms (0.7%)

Memory

-20.0MiB live, 18.6MiB 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
▶	74.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	52.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	73.9%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
▶	50.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify217.0ms (4.6%)

Memory

23.8MiB live, 146.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

6 018×	`lower-*.f64`
6 018×	`lower-*.f32`
3 276×	`cube-prod`
2 776×	`lower-/.f32`
2 766×	`lower-/.f64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	13	63
0	19	65
1	24	65
2	27	61
3	30	61
4	47	61
5	52	61
6	62	61
7	70	61
8	83	61
9	107	60
10	117	60
11	194	60
12	1141	60
13	2080	60
14	2692	60
15	3300	60
16	3946	60
17	4654	60
18	4905	60
19	5096	60
20	5254	60
21	5398	60
22	5590	60
23	6343	60
24	7491	60
25	7918	60
0	8054	60

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

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

localize236.0ms (5%)

Memory

-12.8MiB live, 25.2MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	16.646492131228946	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
accuracy	16.646492131228946	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	30.213327199979616	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0.08984375	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
accuracy	16.606680017283328	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	31.569729828041982	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Samples

18.0ms

256×

valid

Compiler

Compiled 65 to 10 computations (84.6% saved)

Precisions

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

ival-div: 6.0ms (61% of total)

ival-mult: 2.0ms (20.3% of total)

ival-add: 1.0ms (10.2% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

8 → 96

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

((/ x (+ (* x x) 1)) (/ 1 x) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)))

1.0ms

inf

((/ x (+ (* x x) 1)) (/ 1 x) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)))

1.0ms

((/ x (+ (* x x) 1)) (/ 1 x) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)))

simplify323.0ms (6.9%)

Memory

-4.7MiB live, 201.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 624×	`lower-fma.f64`
16 624×	`lower-fma.f32`
3 252×	`lower-*.f64`
3 252×	`lower-*.f32`
1 830×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	760
1	138	752
2	321	720
3	910	686
4	2454	678
5	6072	678
0	8116	660

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 90

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

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

rewrite316.0ms (6.7%)

Memory

29.6MiB live, 282.3MiB allocated

Rules

4 770×	`lower-*.f64`
4 770×	`lower-*.f32`
4 370×	`lower-fma.f32`
4 368×	`lower-fma.f64`
3 720×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	51
0	19	49
1	65	49
2	351	49
3	3035	48
0	9522	48

Stop Event

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

Counts

8 → 573

Calls

Call 1

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

Outputs
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eval283.0ms (6%)

Memory: -25.9MiB live, 156.3MiB allocated
Compiler: Compiled 11 359 to 1 439 computations (87.3% saved)

prune38.0ms (0.8%)

Memory

5.9MiB live, 48.3MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	773	1	774
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	774	4	778

Accuracy

100.0%

Counts

778 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	52.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
✓	50.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify4.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

8×	`lower-+.f32`
6×	`lower-+.f64`
6×	`lower-/.f32`
4×	`lift-/.f64`
4×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
0	12	38
1	16	38
0	16	36

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize47.0ms (1%)

Memory

-4.4MiB live, 32.5MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

41.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

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

ival-div: 5.0ms (52.1% of total)

ival-add: 2.0ms (20.8% of total)

ival-mult: 2.0ms (20.8% 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

4.0MiB live, 4.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

1.0ms

-inf

((/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (+ (/ 1 x) x) (/ 1 x))

0.0ms

inf

((/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (+ (/ 1 x) x) (/ 1 x))

0.0ms

((/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (+ (/ 1 x) x) (/ 1 x))

simplify222.0ms (4.7%)

Memory

-26.0MiB live, 128.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	334
1	132	308
2	309	300
3	875	272
4	2390	270
5	5580	270
6	7731	270
0	8165	260

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 43

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

rewrite184.0ms (3.9%)

Memory

9.4MiB live, 133.8MiB allocated

Rules

2 714×	`lower-fma.f64`
2 714×	`lower-fma.f32`
2 174×	`lower-*.f64`
2 174×	`lower-*.f32`
2 046×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	36
0	12	36
1	61	36
2	423	32
0	4327	32

Stop Event

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

Counts

4 → 254

Calls

Call 1

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

Outputs
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eval35.0ms (0.7%)

Memory: 17.3MiB live, 88.9MiB allocated
Compiler: Compiled 4 875 to 1 045 computations (78.6% saved)

prune7.0ms (0.1%)

Memory

-11.0MiB live, 26.7MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	297	4	301

Accuracy

100.0%

Counts

301 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	52.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
✓	50.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 59 to 34 computations (42.4% saved)

regimes6.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Counts

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes33.0ms (0.7%)

Memory

-28.5MiB live, 24.9MiB 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:

31.0ms	x
2.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB 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
81.4%	3	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.5%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
50.7%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
50.7%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch2.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	57222488.08368402	190675640199.0283

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)

bsearch16.0ms (0.3%)

Memory

-1.1MiB live, 34.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	8.153596126212868e-8	32.18944704775416

Samples

9.0ms

144×

valid

Compiler

Compiled 82 to 99 computations (-20.7% saved)

Precisions

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

ival-mult: 5.0ms (74.9% of total)

ival-div: 1.0ms (15% of total)

ival-add: 1.0ms (15% of total)

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

exact: 0.0ms (0% of total)

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

simplify23.0ms (0.5%)

Memory

13.6MiB live, 91.2MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	71
1	24	71

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.1s (24.3%)

Memory

-20.9MiB live, 375.0MiB allocated

Rules

16 624×	`lower-fma.f64`
16 624×	`lower-fma.f32`
12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
4 942×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	760
1	138	752
2	321	720
3	910	686
4	2454	678
5	6072	678
0	8116	660
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	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13

Stop Event

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

Compiler

Compiled 94 to 50 computations (46.8% saved)

preprocess284.0ms (6%)

Memory: -1.0MiB live, 152.2MiB allocated
Compiler: Compiled 132 to 70 computations (47% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze0.0ms (0%)

sample609.0ms (12.9%)

explain185.0ms (3.9%)

preprocess20.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.2%)

localize15.0ms (0.3%)

series3.0ms (0.1%)

simplify177.0ms (3.8%)

rewrite181.0ms (3.8%)

eval43.0ms (0.9%)

prune31.0ms (0.7%)

simplify217.0ms (4.6%)

localize236.0ms (5%)

series5.0ms (0.1%)

simplify323.0ms (6.9%)

rewrite316.0ms (6.7%)

eval283.0ms (6%)

prune38.0ms (0.8%)

simplify4.0ms (0.1%)

localize47.0ms (1%)

series3.0ms (0.1%)

simplify222.0ms (4.7%)

rewrite184.0ms (3.9%)

eval35.0ms (0.7%)

prune7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes33.0ms (0.7%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch2.0ms (0%)

bsearch16.0ms (0.3%)

simplify23.0ms (0.5%)

soundness1.1s (24.3%)

preprocess284.0ms (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