Metrics for Asymptote B

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample864.0ms (20.3%)

Memory

39.8MiB live, 1 061.2MiB allocated

Samples

614.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 400.0ms

ival-div: 245.0ms (61.2% of total)

ival-add: 90.0ms (22.5% of total)

ival-sub: 50.0ms (12.5% of total)

ival-true: 6.0ms (1.5% of total)

exact: 6.0ms (1.5% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

explain89.0ms (2.1%)

Memory

-24.2MiB live, 191.3MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

31.0ms

512×

valid

Compiler

Compiled 73 to 25 computations (65.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-div: 7.0ms (43.4% of total)

ival-add: 5.0ms (31% of total)

ival-sub: 3.0ms (18.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess20.0ms (0.5%)

Memory

-21.0MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	25	24
2	63	22
3	138	22
4	258	22
5	428	22
6	457	22
7	471	22
8	484	22
0	7	11
0	12	11
1	19	11
2	20	11
0	20	11

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
0	12	29
1	19	29
2	20	29
0	20	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize68.0ms (1.6%)

Memory

-4.9MiB live, 33.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.01171875	(/.f64 x (+.f64 x #s(literal 1 binary64)))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))
accuracy	0.01953125	(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))

Samples

14.0ms

256×

valid

Compiler

Compiled 31 to 9 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 3.0ms (39.3% of total)

ival-sub: 2.0ms (26.2% of total)

ival-add: 2.0ms (26.2% 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

6.1MiB live, 6.2MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

simplify149.0ms (3.5%)

Memory

16.1MiB live, 166.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	387
1	211	385
2	469	374
3	1228	354
4	3217	348
5	6371	346
6	7705	346
0	8035	338

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 55

Calls

Call 1

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

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

rewrite170.0ms (4%)

Memory

22.2MiB live, 216.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	12	27
1	66	27
2	701	27
0	9606	27

Stop Event

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

Counts

5 → 561

Calls

Call 1

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

Outputs
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eval446.0ms (10.5%)

Memory: -223.7MiB live, 173.7MiB allocated
Compiler: Compiled 14 411 to 1 738 computations (87.9% saved)

prune12.0ms (0.3%)

Memory

-1.5MiB live, 37.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	611	5	616
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	612	5	617

Accuracy

100.0%

Counts

617 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.2%	(/.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x (-.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
▶	54.3%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64)))
▶	45.1%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
▶	45.3%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal 1 binary64))
▶	54.1%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal -1 binary64))

Compiler

Compiled 64 to 54 computations (15.6% saved)

simplify157.0ms (3.7%)

Memory

15.3MiB live, 202.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	129
0	34	129
1	55	129
2	87	127
3	181	123
4	354	123
5	1423	119
6	5980	119
0	8158	113

Stop Event

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

Calls

Call 1

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

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

localize53.0ms (1.3%)

Memory

-1.2MiB live, 80.6MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.48932925343677786	(/.f64 #s(literal 2 binary64) (*.f64 x x))
accuracy	35.13309677526536	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64))
accuracy	0	(*.f64 x x)
accuracy	29.239268040708545	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64)))
accuracy	35.00437267184615	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal 1 binary64))
accuracy	29.360457890124483	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal -1 binary64))
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(-.f64 x #s(literal -1 binary64))
accuracy	0.00390625	(fma.f64 (-.f64 x #s(literal 1 binary64)) x (-.f64 x #s(literal -1 binary64)))
accuracy	14.781417814100346	(/.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x (-.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))

Samples

34.0ms

256×

valid

Compiler

Compiled 117 to 22 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-div: 8.0ms (34.7% of total)

ival-add: 7.0ms (30.3% of total)

ival-mult: 5.0ms (21.7% of total)

ival-sub: 3.0ms (13% of total)

exact: 1.0ms (4.3% of total)

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

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

series8.0ms (0.2%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

12 → 144

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((+ (* (- x 1) x) (- x -1)) (/ (+ (* (- x 1) x) (- x -1)) (+ (* x x) -1)) (- x 1) (- x -1) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (* (* x x) -2) -1) (* x x) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 2 (* x x)) 1) (/ 2 (* x x)))
1.0ms	x	@	inf	((+ (* (- x 1) x) (- x -1)) (/ (+ (* (- x 1) x) (- x -1)) (+ (* x x) -1)) (- x 1) (- x -1) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (* (* x x) -2) -1) (* x x) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 2 (* x x)) 1) (/ 2 (* x x)))
1.0ms	x	@	-inf	((+ (* (- x 1) x) (- x -1)) (/ (+ (* (- x 1) x) (- x -1)) (+ (* x x) -1)) (- x 1) (- x -1) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (* (* x x) -2) -1) (* x x) (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 2 (* x x)) 1) (/ 2 (* x x)))

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify178.0ms (4.2%)

Memory

8.8MiB live, 200.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	958
1	114	958
2	263	958
3	622	938
4	1430	928
5	5392	922
0	8300	879

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 140

Calls

Call 1

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

rewrite155.0ms (3.6%)

Memory

9.0MiB live, 278.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	111
0	34	111
1	169	109
2	1647	109
0	8383	107

Stop Event

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

Counts

12 → 486

Calls

Call 1

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

Outputs
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eval81.0ms (1.9%)

Memory: 1.2MiB live, 155.7MiB allocated
Compiler: Compiled 12 958 to 1 663 computations (87.2% saved)

prune13.0ms (0.3%)

Memory

-0.2MiB live, 38.1MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	647	1	648
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	648	5	653

Accuracy

100.0%

Counts

653 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.2%	(/.f64 #s(approx (+ (* (- x 1) x) (- x -1)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
✓	54.3%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64)))
✓	45.1%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
✓	45.3%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal 1 binary64))
✓	54.1%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal -1 binary64))

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify241.0ms (5.7%)

Memory

-17.3MiB live, 161.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	44
0	15	44
1	28	44
2	51	40
3	120	34
4	229	34
5	858	34
6	2888	34
7	4495	34
8	5755	34
9	6548	34
10	6880	34
11	7057	34
12	7147	34
13	7922	34
0	8141	34

Stop Event

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

Calls

Call 1

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

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

localize28.0ms (0.7%)

Memory

-0.2MiB live, 37.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	#s(approx (+ (* (- x 1) x) (- x -1)) (fma.f64 x x #s(literal 1 binary64)))
accuracy	14.781417814100346	(/.f64 #s(approx (+ (* (- x 1) x) (- x -1)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))

Samples

21.0ms

256×

valid

Compiler

Compiled 39 to 13 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 3.0ms (25.3% of total)

ival-add: 3.0ms (25.3% of total)

ival-mult: 3.0ms (25.3% of total)

ival-div: 2.0ms (16.8% 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

4.1MiB live, 4.1MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

0.0ms

inf

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

0.0ms

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

simplify152.0ms (3.6%)

Memory

-12.2MiB live, 141.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	276
1	76	276
2	163	276
3	382	272
4	809	270
5	1335	270
6	2915	270
7	5617	270
8	7809	270
0	8060	234

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite173.0ms (4.1%)

Memory

9.4MiB live, 209.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
0	15	41
1	84	41
2	681	37
0	9167	35

Stop Event

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

Counts

4 → 646

Calls

Call 1

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

Outputs
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eval82.0ms (1.9%)

Memory: 10.6MiB live, 132.6MiB allocated
Compiler: Compiled 16 584 to 2 008 computations (87.9% saved)

prune33.0ms (0.8%)

Memory

1.8MiB live, 38.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	694	0	694
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	694	5	699

Accuracy

100.0%

Counts

699 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.2%	(/.f64 #s(approx (+ (* (- x 1) x) (- x -1)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
✓	54.3%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64)))
✓	45.1%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
✓	45.3%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal 1 binary64))
✓	54.1%	#s(approx (+ (/ 1 (- x 1)) (/ x (+ x 1))) #s(literal -1 binary64))

Compiler

Compiled 82 to 51 computations (37.8% saved)

regimes6.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	3	`x`
98.9%	2	`(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes2.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
98.6%	2	`(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes51.0ms (1.2%)

Memory

-40.0MiB live, 48.6MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

49.0ms	(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))
2.0ms	x

Results

Accuracy	Segments	Branch
98.4%	3	`x`
98.4%	2	`(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

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

Results

Accuracy	Segments	Branch
97.9%	2	`(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
54.1%	1	`x`
54.1%	1	`(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (/.f64 x (+.f64 x #s(literal 1 binary64))))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	0.9999999999999999

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	0.9999999999999999

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	0.9999999999999999

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	-1.0	0.9999999999999999

Samples

0.0ms

16×

valid

Compiler

Compiled 18 to 19 computations (-5.6% saved)

Precisions

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

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

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

simplify25.0ms (0.6%)

Memory

9.9MiB live, 48.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	212
1	43	212
2	46	212
3	51	212

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness866.0ms (20.3%)

Memory

-6.2MiB live, 497.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	12	27
1	66	27
2	701	27
0	9606	27
0	48	958
1	114	958
2	263	958
3	622	938
4	1430	928
5	5392	922
0	8300	879
0	83	387
1	211	385
2	469	374
3	1228	354
4	3217	348
5	6371	346
6	7705	346
0	8035	338

Stop Event

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

Compiler

Compiled 178 to 75 computations (57.9% saved)

preprocess112.0ms (2.6%)

Memory: 2.0MiB live, 112.5MiB allocated
Compiler: Compiled 252 to 68 computations (73% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	9	29
1	25	24
2	63	22
3	138	22
4	258	22
5	428	22
6	457	22
7	471	22
8	484	22
0	7	11
0	12	11
1	19	11
2	20	11
0	20	11

Iter	Nodes	Cost
0	9	29
1	25	24
2	63	22
3	138	22
4	258	22
5	428	22
6	457	22
7	471	22
8	484	22
0	7	11
0	12	11
1	19	11
2	20	11
0	20	11

start0.0ms (0%)

analyze2.0ms (0.1%)

sample864.0ms (20.3%)

explain89.0ms (2.1%)

preprocess20.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize68.0ms (1.6%)

series4.0ms (0.1%)

simplify149.0ms (3.5%)

rewrite170.0ms (4%)

eval446.0ms (10.5%)

prune12.0ms (0.3%)

simplify157.0ms (3.7%)

localize53.0ms (1.3%)

series8.0ms (0.2%)

simplify178.0ms (4.2%)

rewrite155.0ms (3.6%)

eval81.0ms (1.9%)

prune13.0ms (0.3%)

simplify241.0ms (5.7%)

localize28.0ms (0.7%)

series3.0ms (0.1%)

simplify152.0ms (3.6%)

rewrite173.0ms (4.1%)

eval82.0ms (1.9%)

prune33.0ms (0.8%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes2.0ms (0.1%)

regimes51.0ms (1.2%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

simplify25.0ms (0.6%)

soundness866.0ms (20.3%)

preprocess112.0ms (2.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	29
1	25	24
2	63	22
3	138	22
4	258	22
5	428	22
6	457	22
7	471	22
8	484	22
0	7	11
0	12	11
1	19	11
2	20	11
0	20	11