Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample622.0ms (8.7%)

Memory

25.1MiB live, 701.2MiB allocated

Samples

347.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 186.0ms

ival-mult: 65.0ms (34.9% of total)

ival-div: 62.0ms (33.2% of total)

ival-add: 45.0ms (24.1% of total)

ival-true: 6.0ms (3.2% of total)

exact: 5.0ms (2.7% of total)

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

Bogosity

explain184.0ms (2.6%)

Memory

36.5MiB live, 75.1MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	n/o	57	0
↳	`(*.f64 x x)`	overflow	57
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	57

Confusion

	Predicted +	Predicted -
+	57	0
-	0	199

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	57	0	0
-	0	0	199

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	199
1	57

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 62 to 24 computations (61.3% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

preprocess37.0ms (0.5%)

Memory

-8.5MiB live, 29.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.2%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize22.0ms (0.3%)

Memory

-19.3MiB live, 21.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	13.320354124619504	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

17.0ms

256×

valid

Compiler

Compiled 36 to 12 computations (66.7% saved)

Precisions

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

ival-div: 7.0ms (60.8% of total)

ival-add: 2.0ms (17.4% of total)

ival-mult: 2.0ms (17.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

Calls

3 calls:

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

simplify160.0ms (2.2%)

Memory

23.0MiB live, 132.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	226
1	131	224
2	312	216
3	883	212
4	2385	210
5	5560	210
6	7661	210
0	8081	197

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 35

Calls

Call 1

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

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

rewrite170.0ms (2.4%)

Memory

-4.1MiB live, 232.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 327

Calls

Call 1

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

Outputs
#<batchref>
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eval43.0ms (0.6%)

Memory: 2.0MiB live, 76.7MiB allocated
Compiler: Compiled 7 796 to 1 076 computations (86.2% saved)

prune53.0ms (0.7%)

Memory

-21.9MiB live, 39.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

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

Accuracy

100.0%

Counts

363 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.7%	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
▶	79.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	54.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	79.1%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
▶	48.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
	53.3%	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))

Compiler

Compiled 114 to 64 computations (43.9% saved)

simplify371.0ms (5.2%)

Memory

15.7MiB live, 171.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	320	(/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)
cost-diff	320	(-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
cost-diff	1216	(*.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
cost-diff	1472	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	192	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
cost-diff	512	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
cost-diff	0	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
cost-diff	0	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	0	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	146
0	36	102
1	64	102
2	144	102
3	371	102
4	1487	96
5	5488	96
0	8324	95

Stop Event

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

Calls

Call 1

Inputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
x
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
x
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
#s(literal 1 binary64)
(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
(fma.f64 x x #s(literal 1 binary64))
x
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
(-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(*.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
#s(literal 0 binary64)
(/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)
(fma.f64 (neg.f64 x) x #s(literal -1 binary64))
(neg.f64 x)
x
#s(literal -1 binary64)
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))

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

localize84.0ms (1.2%)

Memory

-6.9MiB live, 69.2MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.05078125	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
accuracy	13.303833193967177	(/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)
accuracy	19.139928338493423	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0.07421875	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
accuracy	13.303833193967177	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
accuracy	13.320354124619504	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	28.94985635584014	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	32.88748564766172	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	13.320354124619504	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

48.0ms

256×

valid

Compiler

Compiled 291 to 39 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-div: 9.0ms (45.5% of total)

ival-mult: 6.0ms (30.3% of total)

ival-add: 2.0ms (10.1% of total)

ival-sub: 1.0ms (5.1% of total)

ival-neg: 1.0ms (5.1% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

20.9MiB live, 20.8MiB allocated

Counts

14 → 168

Calls

Call 1

Inputs
#s(alt (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)) (patch #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) (patch (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x x) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) (patch (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))) (patch (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (patch (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (patch (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x) (patch (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (patch (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (/ (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x))) (* 0 (/ (+ (* (neg x) x) -1) x)) (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (/ (+ (* (neg x) x) -1) x) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (neg x))
2.0ms	x	@	0	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (/ (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x))) (* 0 (/ (+ (* (neg x) x) -1) x)) (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (/ (+ (* (neg x) x) -1) x) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (neg x))
1.0ms	x	@	inf	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (/ (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x))) (* 0 (/ (+ (* (neg x) x) -1) x)) (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (/ (+ (* (neg x) x) -1) x) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (neg x))

Time

Variable

Point

Expression

2.0ms

-inf

((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (/ (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x))) (* 0 (/ (+ (* (neg x) x) -1) x)) (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (/ (+ (* (neg x) x) -1) x) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (neg x))

2.0ms

((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (/ (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x))) (* 0 (/ (+ (* (neg x) x) -1) x)) (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (/ (+ (* (neg x) x) -1) x) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (neg x))

1.0ms

inf

((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ 1 (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x) (/ (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x))) (* 0 (/ (+ (* (neg x) x) -1) x)) (- (* 0 (/ (+ (* (neg x) x) -1) x)) (+ (* (neg x) x) -1)) (/ (+ (* (neg x) x) -1) x) (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (neg x))

simplify435.0ms (6.1%)

Memory

7.0MiB live, 197.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	1199
1	212	1159
2	555	1124
3	1795	1052
4	6266	1052
0	8257	1010

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 161

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
0
0
0
0
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(/ -1 x)
(/ (- (* -1 (pow x 2)) 1) x)
(/ (- (* -1 (pow x 2)) 1) x)
(/ (- (* -1 (pow x 2)) 1) x)
(/ 1 x)
(/ (+ 1 (* 2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (+ 2 (pow x 2)))) x)
(/ (+ 1 (* (pow x 2) (+ 2 (pow x 2)))) x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
0
0
0
0
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (/ 1 (pow x 2)))))
(* -1 (* x (+ 1 (/ 1 (pow x 2)))))
(* -1 (* x (+ 1 (/ 1 (pow x 2)))))
(pow x 3)
(* (pow x 3) (+ 1 (* 2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1 (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 3) (+ 1 (+ (* 2 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
0
0
0
0
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (/ 1 (pow x 2)))))
(* -1 (* x (+ 1 (/ 1 (pow x 2)))))
(* -1 (* x (+ 1 (/ 1 (pow x 2)))))
(pow x 3)
(* (pow x 3) (+ 1 (* 2 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 2 (/ 1 (pow x 2))) (pow x 2))) 1)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

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

rewrite389.0ms (5.5%)

Memory

-11.9MiB live, 310.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	126
0	36	81
1	139	77
2	1062	72
0	10527	72

Stop Event

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

Counts

14 → 3 677

Calls

Call 1

Inputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
(*.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
(-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)
(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
(neg.f64 x)

Outputs
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eval1.5s (20.9%)

Memory: 24.7MiB live, 1 383.7MiB allocated
Compiler: Compiled 151 638 to 8 972 computations (94.1% saved)

prune90.0ms (1.3%)

Memory

28.0MiB live, 301.3MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	4 952	2	4 954
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	4 955	5	4 960

Accuracy

100.0%

Counts

4 960 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.7%	(/.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
✓	79.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	54.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
✓	48.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 40 to 28 computations (30% saved)

simplify309.0ms (4.3%)

Memory

-46.9MiB live, 185.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	256	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
cost-diff	320	(/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)
cost-diff	1472	(/.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	0	(-.f64 x (/.f64 #s(literal -1 binary64) x))
cost-diff	0	#s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	89
0	26	89
1	41	89
2	75	89
3	149	89
4	368	79
5	1160	70
6	3238	70
7	7338	70
0	8087	69

Stop Event

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

Calls

Call 1

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

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

localize44.0ms (0.6%)

Memory

20.0MiB live, 141.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.05078125	(*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
accuracy	13.303833193967177	(/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)
accuracy	19.139928338493423	(/.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)))
accuracy	0	(/.f64 #s(literal -1 binary64) x)
accuracy	0	#s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x)))
accuracy	0.0078125	(-.f64 x (/.f64 #s(literal -1 binary64) x))
accuracy	0.07421875	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))

Samples

33.0ms

256×

valid

Compiler

Compiled 166 to 30 computations (81.9% saved)

Precisions

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

ival-div: 11.0ms (48.4% of total)

ival-mult: 5.0ms (22% of total)

ival-add: 2.0ms (8.8% of total)

ival-neg: 2.0ms (8.8% of total)

ival-sub: 1.0ms (4.4% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

-22.9MiB live, 14.6MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify149.0ms (2.1%)

Memory

28.6MiB live, 148.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	737
1	212	721
2	555	692
3	1802	614
4	6196	614
0	8189	590

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 102

Calls

Call 1

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

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

rewrite269.0ms (3.8%)

Memory

-13.1MiB live, 138.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	78
0	26	78
1	108	70
2	835	58
0	9792	58

Stop Event

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

Counts

9 → 1 312

Calls

Call 1

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

Outputs
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eval827.0ms (11.6%)

Memory: 7.9MiB live, 434.7MiB allocated
Compiler: Compiled 34 730 to 3 860 computations (88.9% saved)

prune25.0ms (0.3%)

Memory

11.1MiB live, 87.4MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	1 451	1	1 452
Fresh	0	0	0
Picked	1	1	2
Done	0	3	3
Total	1 452	5	1 457

Accuracy

100.0%

Counts

1 457 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.7%	(/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(approx (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (fma.f64 (fma.f64 x x #s(literal 2 binary64)) x (/.f64 #s(literal 1 binary64) x))))
✓	79.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	54.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
✓	48.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 37 to 28 computations (24.3% saved)

simplify132.0ms (1.8%)

Memory

28.5MiB live, 178.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	78
0	22	78
1	36	74
2	66	74
3	152	74
4	371	70
5	1044	66
6	2576	66
7	5722	66
8	7892	66
0	8149	66

Stop Event

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

Calls

Call 1

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

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

localize68.0ms (1%)

Memory

-36.1MiB live, 97.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	#s(approx (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (fma.f64 (fma.f64 x x #s(literal 2 binary64)) x (/.f64 #s(literal 1 binary64) x)))
accuracy	0.0546875	(fma.f64 (fma.f64 x x #s(literal 2 binary64)) x (/.f64 #s(literal 1 binary64) x))
accuracy	19.139928338493423	(/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(approx (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (fma.f64 (fma.f64 x x #s(literal 2 binary64)) x (/.f64 #s(literal 1 binary64) x))))

Samples

42.0ms

256×

valid

Compiler

Compiled 113 to 27 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 9.0ms (45.5% of total)

ival-div: 4.0ms (20.2% of total)

ival-add: 4.0ms (20.2% of total)

ival-neg: 1.0ms (5.1% 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

10.0MiB live, 10.0MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

simplify127.0ms (1.8%)

Memory

17.6MiB live, 165.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	494
1	192	486
2	498	452
3	1629	416
4	6515	416
0	8130	377

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

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

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

rewrite145.0ms (2%)

Memory

2.6MiB live, 221.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	71
0	22	71
1	104	59
2	845	59
0	8999	59

Stop Event

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

Counts

5 → 340

Calls

Call 1

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

Outputs
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eval90.0ms (1.3%)

Memory: -30.3MiB live, 224.0MiB allocated
Compiler: Compiled 10 205 to 1 214 computations (88.1% saved)

prune10.0ms (0.1%)

Memory

-11.9MiB live, 26.9MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	399	0	399
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	399	5	404

Accuracy

100.0%

Counts

404 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.7%	(/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(approx (* (+ (* (neg x) x) -1) (/ (+ (* (neg x) x) -1) x)) (fma.f64 (fma.f64 x x #s(literal 2 binary64)) x (/.f64 #s(literal 1 binary64) x))))
✓	79.2%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	54.6%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
✓	48.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 142 to 64 computations (54.9% saved)

regimes7.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

-30.8MiB live, 7.4MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
79.7%	4	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.2%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
48.6%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
48.6%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch3.0ms (0%)

Memory

3.9MiB live, 3.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
2.0ms	50534.971955151246	1644184546.1571143

Samples

1.0ms

32×

valid

Compiler

Compiled 30 to 29 computations (3.3% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch12.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.0180420038374732e-6	1.1123672507168159

Samples

6.0ms

144×

valid

Compiler

Compiled 82 to 99 computations (-20.7% saved)

Precisions

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

ival-div: 1.0ms (34.7% of total)

ival-add: 1.0ms (34.7% of total)

ival-mult: 1.0ms (34.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify24.0ms (0.3%)

Memory

0.9MiB live, 39.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	71
1	27	71
2	34	71
3	40	71
4	44	71
5	46	71

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
(if (<=.f64 x #s(literal 10000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Outputs
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (-.f64 x (/.f64 #s(literal -1 binary64) x))))
(if (<=.f64 x #s(literal 10000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

soundness554.0ms (7.8%)

Memory

-4.1MiB live, 386.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13
0	74	1199
1	212	1159
2	555	1124
3	1795	1052
4	6266	1052
0	8257	1010
0	45	226
1	131	224
2	312	216
3	883	212
4	2385	210
5	5560	210
6	7661	210
0	8081	197

Stop Event

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

Compiler

Compiled 94 to 53 computations (43.6% saved)

preprocess143.0ms (2%)

Memory: 26.1MiB live, 142.2MiB allocated
Compiler: Compiled 132 to 74 computations (43.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze0.0ms (0%)

sample622.0ms (8.7%)

explain184.0ms (2.6%)

preprocess37.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize22.0ms (0.3%)

series3.0ms (0%)

simplify160.0ms (2.2%)

rewrite170.0ms (2.4%)

eval43.0ms (0.6%)

prune53.0ms (0.7%)

simplify371.0ms (5.2%)

localize84.0ms (1.2%)

series10.0ms (0.1%)

simplify435.0ms (6.1%)

rewrite389.0ms (5.5%)

eval1.5s (20.9%)

prune90.0ms (1.3%)

simplify309.0ms (4.3%)

localize44.0ms (0.6%)

series7.0ms (0.1%)

simplify149.0ms (2.1%)

rewrite269.0ms (3.8%)

eval827.0ms (11.6%)

prune25.0ms (0.3%)

simplify132.0ms (1.8%)

localize68.0ms (1%)

series4.0ms (0.1%)

simplify127.0ms (1.8%)

rewrite145.0ms (2%)

eval90.0ms (1.3%)

prune10.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

regimes3.0ms (0%)

bsearch3.0ms (0%)

bsearch12.0ms (0.2%)

simplify24.0ms (0.3%)

soundness554.0ms (7.8%)

preprocess143.0ms (2%)

end0.0ms (0%)

Profiling

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