Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample717.0ms (13%)

Memory

55.6MiB live, 631.3MiB allocated

Samples

318.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-mult: 60.0ms (36% of total)

ival-div: 57.0ms (34.2% of total)

ival-add: 37.0ms (22.2% of total)

ival-true: 5.0ms (3% of total)

exact: 5.0ms (3% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain128.0ms (2.3%)

Memory

-25.4MiB live, 134.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
59	-	-	`(/.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	59	0
↳	`(*.f64 x x)`	overflow	59
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	59

Confusion

	Predicted +	Predicted -
+	59	0
-	0	197

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	59	0	0
-	0	0	197

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	197
1	59

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 79 to 32 computations (59.5% saved)

Precisions

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

ival-mult: 4.0ms (37.6% of total)

ival-div: 3.0ms (28.2% 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)

preprocess19.0ms (0.3%)

Memory

17.7MiB live, 17.7MiB 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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.4%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB 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)

localize19.0ms (0.3%)

Memory

-16.3MiB live, 21.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	13.799648805576062	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

15.0ms

256×

valid

Compiler

Compiled 36 to 12 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (34.1% of total)

ival-add: 2.0ms (34.1% of total)

ival-mult: 2.0ms (34.1% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

3 → 15

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

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))

simplify154.0ms (2.8%)

Memory

28.6MiB live, 141.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	149
1	131	147
2	312	139
3	883	135
4	2391	133
5	5547	133
6	7623	133
0	8043	127

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

Calls

Call 1

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

Outputs
1
#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) (+ 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)
(* -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)

rewrite211.0ms (3.8%)

Memory

-3.9MiB live, 223.3MiB 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
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))) (pow.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))))
(.f64 (-.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -3 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))))
(.f64 (.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))))
(.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))))
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(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (/.f64 x (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))))) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (neg.f64 x))) (*.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 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 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(/.f64 (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) x)) (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))
(/.f64 (.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64)))) (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(/.f64 (.f64 x (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) x) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(/.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal -1 binary64))))
(/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) x))
(/.f64 (neg.f64 x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (.f64 x (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))) (.f64 x (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 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)))
(neg.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(fma.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 x x) (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64)) (*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(fma.f64 (.f64 x x) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64))) (/.f64 (/.f64 (*.f64 x x) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x x) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (*.f64 #s(literal -1 binary64) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))))
(+.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 x x)) (*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))))
(+.f64 (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval89.0ms (1.6%)

Memory: -7.1MiB live, 89.5MiB allocated
Compiler: Compiled 7 652 to 1 078 computations (85.9% saved)

prune33.0ms (0.6%)

Memory

-17.0MiB live, 21.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	332	5	337
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	333	5	338

Accuracy

100.0%

Counts

338 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	51.4%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	78.4%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
▶	51.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	50.7%	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))

Compiler

Compiled 94 to 66 computations (29.8% saved)

simplify189.0ms (3.4%)

Memory

20.8MiB live, 139.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	(-.f64 x (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	192	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
cost-diff	512	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
cost-diff	0	#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: 10 (0.0ms)

Iter	Nodes	Cost
0	17	85
0	25	83
1	34	83
2	49	83
3	66	83
4	121	83
5	210	83
6	363	83
7	651	83
8	1187	83
9	2142	83
10	3272	82
11	4409	82
12	5544	82
13	6254	82
14	6699	82
15	7127	82
16	7847	82
0	8138	82

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
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
x
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)

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
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
x
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)

localize229.0ms (4.1%)

Memory

9.5MiB live, 47.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.00390625	(-.f64 x (pow.f64 x #s(literal 3 binary64)))
accuracy	31.569533996229463	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0.09375	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
accuracy	13.75192042683724	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
accuracy	13.799648805576062	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	30.958190071241134	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	30.93334159834112	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	13.799648805576062	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

219.0ms

256×

valid

Compiler

Compiled 171 to 31 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 209.0ms

ival-sub: 197.0ms (94.2% of total)

ival-div: 6.0ms (2.9% of total)

ival-pow: 3.0ms (1.4% of total)

ival-mult: 2.0ms (1% of total)

ival-add: 1.0ms (0.5% of total)

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

exact: 0.0ms (0% of total)

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

series40.0ms (0.7%)

Memory

-25.2MiB live, 12.2MiB allocated

Counts

11 → 21

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)
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))

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

Calls

3 calls:

Time	Variable		Point	Expression
37.0ms	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) (/ x (+ (* x x) 1)) (- x (pow x 3)) (pow x 3))
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) (/ x (+ (* x x) 1)) (- x (pow x 3)) (pow x 3))
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) (/ x (+ (* x x) 1)) (- x (pow x 3)) (pow x 3))

Time

Variable

Point

Expression

37.0ms

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

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

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

simplify232.0ms (4.2%)

Memory

-2.5MiB live, 234.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	186
1	153	174
2	375	170
3	1190	162
4	4420	162
0	8215	152

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 20

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

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 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (pow x 2)) x)
(+.f64 (/.f64 #s(literal 1 binary64) x) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 (/.f64 #s(literal 1 binary64) x) x)
(* -1 (pow x 3))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))

rewrite209.0ms (3.8%)

Memory

18.5MiB live, 240.2MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	71
0	25	69
1	91	69
2	521	69
3	4782	68
0	9077	68

Stop Event

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

Counts

11 → 781

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)
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))

Outputs
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 (/.f64 x (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 (/.f64 x (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)))) (-.f64 (fma.f64 x x (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 x x) (*.f64 x (-.f64 x (pow.f64 x #s(literal 5 binary64))))) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (neg.f64 x)))
(*.f64 (pow.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(*.f64 (/.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 x) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) x)
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(*.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 x (pow.f64 x #s(literal 3 binary64)))))
(*.f64 (sqrt.f64 x) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(.f64 (/.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 x (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 x (pow.f64 x #s(literal 3 binary64)))))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) x)) #s(literal -1 binary64))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) x)
(*.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))))
(*.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) x)))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x x) (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 x (/.f64 x (+.f64 (pow.f64 x #s(literal 3 binary64)) x)))
(*.f64 x (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 x (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 x (+.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
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(fma.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64) x)
(fma.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) x (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (/.f64 x (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (neg.f64 x) (*.f64 x x) x)
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) x)
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (*.f64 x x) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (*.f64 x x) (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(fma.f64 (*.f64 x x) (pow.f64 x #s(literal -1 binary64)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(fma.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64))) x)
(fma.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 #s(literal 1 binary64) x (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 x (/.f64 x (+.f64 (pow.f64 x #s(literal 3 binary64)) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 x (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 x (*.f64 (neg.f64 x) x) x)
(fma.f64 x (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(fma.f64 x #s(literal 1 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(-.f64 (+.f64 x #s(literal 0 binary64)) (pow.f64 x #s(literal 3 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 9 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(-.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x)))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (fma.f64 x (+.f64 x (pow.f64 x #s(literal 5 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) x)
(+.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(+.f64 x (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 x #s(literal 9/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 9/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) x)
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))
(.f64 x (.f64 x x))
(pow.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (*.f64 (log.f64 x) #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3/4 binary64))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(/.f64 (pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 (neg.f64 x))) (pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 #s(literal -1 binary64))))
(/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal 4 binary64)) x)
(/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 x x) (pow.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 3 binary64)) (neg.f64 (log.f64 x))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3 binary64)))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (*.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (*.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 3 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))

eval86.0ms (1.6%)

Memory: -2.4MiB live, 201.1MiB allocated
Compiler: Compiled 14 549 to 1 979 computations (86.4% saved)

prune12.0ms (0.2%)

Memory

5.5MiB live, 44.9MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	772	3	775
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	774	6	780

Accuracy

100.0%

Counts

780 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	51.4%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
▶	50.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
✓	51.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	50.7%	#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x))

Compiler

Compiled 71 to 48 computations (32.4% saved)

simplify512.0ms (9.3%)

Memory

18.2MiB live, 134.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(+.f64 (/.f64 #s(literal 1 binary64) x) x)
cost-diff	0	#s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
cost-diff	-5824	(fma.f64 (*.f64 (neg.f64 x) x) x x)
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
cost-diff	-5824	(*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x)
cost-diff	0	(neg.f64 x)
cost-diff	0	(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	98
0	26	98
1	40	98
2	58	90
3	86	90
4	142	90
5	188	90
6	345	90
7	841	90
8	1397	90
9	2779	86
10	4468	86
11	7075	86
0	8170	84

Stop Event

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

Calls

Call 1

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

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

localize60.0ms (1.1%)

Memory

13.8MiB live, 49.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	#s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
accuracy	0.00390625	(+.f64 (/.f64 #s(literal 1 binary64) x) x)
accuracy	0.09375	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
accuracy	0	(*.f64 (neg.f64 x) x)
accuracy	0	(neg.f64 x)
accuracy	0.03515625	(fma.f64 (*.f64 (neg.f64 x) x) x x)
accuracy	31.569533996229463	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
accuracy	0	(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
accuracy	0	(neg.f64 x)
accuracy	0.046875	(*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x)
accuracy	31.569533996229463	#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x))

Samples

27.0ms

256×

valid

Compiler

Compiled 173 to 35 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-div: 6.0ms (33.7% of total)

ival-mult: 6.0ms (33.7% of total)

ival-add: 4.0ms (22.5% of total)

ival-neg: 1.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

11 → 21

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify329.0ms (5.9%)

Memory

-19.3MiB live, 174.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	188
1	152	174
2	364	170
3	1168	162
4	4268	162
0	8169	154

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 20

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

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

rewrite44.0ms (0.8%)

Memory

27.9MiB live, 63.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	91
0	26	91
1	106	87
0	758	83

Stop Event

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

Counts

11 → 147

Calls

Call 1

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

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

eval20.0ms (0.4%)

Memory: -4.4MiB live, 40.3MiB allocated
Compiler: Compiled 2 620 to 454 computations (82.7% saved)

prune5.0ms (0.1%)

Memory

-26.8MiB live, 11.3MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	0	0
Picked	0	3	3
Done	1	2	3
Total	135	6	141

Accuracy

100.0%

Counts

141 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
✓	50.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
✓	51.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	50.7%	#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x))
▶	51.4%	#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 80 to 53 computations (33.8% saved)

simplify220.0ms (4%)

Memory

32.7MiB live, 189.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

cost-diff

#s(approx (+ (* (neg x) x) 1) #s(literal 1 binary64))

cost-diff

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

cost-diff

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
0	12	38
1	22	35
2	28	35
3	39	35
4	52	35
5	72	35
6	131	35
7	341	35
8	619	35
9	1190	35
10	2205	35
11	3228	35
12	4312	35
13	5058	35
14	5919	35
15	6336	35
16	6471	35
17	6702	35
18	7625	35
19	7856	35
0	8088	34

Stop Event

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

Calls

Call 1

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

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

localize25.0ms (0.4%)

Memory

-9.1MiB live, 27.7MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

accuracy

0.046875

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

accuracy

31.569533996229463

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

accuracy

32.02682590672602

#s(approx (+ (* (neg x) x) 1) #s(literal 1 binary64))

Samples

19.0ms

256×

valid

Compiler

Compiled 63 to 23 computations (63.5% saved)

Precisions

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

ival-mult: 5.0ms (50.3% of total)

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

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

ival-neg: 1.0ms (10.1% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

3 → 18

Calls

Call 1

Inputs

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

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

#s(approx (+ (* (neg x) x) 1) #s(literal 1 binary64))

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

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

-inf

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

0.0ms

inf

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

0.0ms

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

simplify198.0ms (3.6%)

Memory

-16.6MiB live, 175.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	172
1	138	158
2	353	154
3	1118	150
4	4011	150
0	8098	142

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 17

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

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 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x 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 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(* -1 (pow x 3))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) x))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))

rewrite224.0ms (4.1%)

Memory

-24.6MiB live, 123.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
0	12	36
1	53	33
2	353	33
3	3945	33
0	9422	29

Stop Event

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

Counts

3 → 4

Calls

Call 1

Inputs

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

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

#s(approx (+ (* (neg x) x) 1) #s(literal 1 binary64))

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

eval2.0ms (0%)

Memory: 3.5MiB live, 3.5MiB allocated
Compiler: Compiled 285 to 62 computations (78.2% saved)

prune4.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	15	6	21

Accuracy

100.0%

Counts

21 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.4%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	99.9%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
✓	50.7%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
✓	51.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	50.7%	#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x))
✓	51.4%	#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 197 to 91 computations (53.8% saved)

regimes7.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

10 → 1

Calls

Call 1

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes8.0ms (0.2%)

Memory

-26.6MiB live, 10.7MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
3.0ms	(/.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)

regimes5.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
80.5%	4	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.7%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.2%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB 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(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x))

Outputs
#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #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
51.4%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
51.4%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch2.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	59446297.18384033	1601199802.9990032

Samples

1.0ms

16×

valid

Compiler

Compiled 27 to 23 computations (14.8% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch22.0ms (0.4%)

Memory

-23.5MiB live, 22.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	0.793800044147743	59446297.18384033

Samples

13.0ms

144×

valid

Compiler

Compiled 244 to 180 computations (26.2% saved)

Precisions

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

ival-div: 1.0ms (35.8% of total)

ival-add: 1.0ms (35.8% of total)

ival-mult: 1.0ms (35.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.793800044147743	59446297.18384033

Compiler

Compiled 244 to 189 computations (22.5% saved)

bsearch5.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	0.793800044147743	59446297.18384033

Samples

2.0ms

48×

valid

Compiler

Compiled 271 to 207 computations (23.6% 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)

simplify23.0ms (0.4%)

Memory

15.7MiB live, 54.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	147
1	47	147
2	51	147
3	54	147
4	55	147

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (neg.f64 x) x) x x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x))

Outputs
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x x) 1) x) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (neg.f64 x) x) x x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x)) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (.f64 #s(approx (+ ( (neg x) x) 1) #s(literal 1 binary64)) x))

soundness1.3s (22.9%)

Memory

34.5MiB live, 679.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	71
0	25	69
1	91	69
2	521	69
3	4782	68
0	9077	68
0	45	149
1	131	147
2	312	139
3	883	135
4	2391	133
5	5547	133
6	7623	133
0	8043	127
0	53	186
1	153	174
2	375	170
3	1190	162
4	4420	162
0	8215	152
0	54	188
1	152	174
2	364	170
3	1168	162
4	4268	162
0	8169	154
0	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13

Stop Event

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

Compiler

Compiled 297 to 138 computations (53.5% saved)

preprocess162.0ms (2.9%)

Memory: -21.7MiB live, 170.1MiB allocated
Compiler: Compiled 364 to 118 computations (67.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

Iter	Nodes	Cost
0	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%)

sample717.0ms (13%)

explain128.0ms (2.3%)

preprocess19.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize19.0ms (0.3%)

series2.0ms (0%)

simplify154.0ms (2.8%)

rewrite211.0ms (3.8%)

eval89.0ms (1.6%)

prune33.0ms (0.6%)

simplify189.0ms (3.4%)

localize229.0ms (4.1%)

series40.0ms (0.7%)

simplify232.0ms (4.2%)

rewrite209.0ms (3.8%)

eval86.0ms (1.6%)

prune12.0ms (0.2%)

simplify512.0ms (9.3%)

localize60.0ms (1.1%)

series5.0ms (0.1%)

simplify329.0ms (5.9%)

rewrite44.0ms (0.8%)

eval20.0ms (0.4%)

prune5.0ms (0.1%)

simplify220.0ms (4%)

localize25.0ms (0.4%)

series1.0ms (0%)

simplify198.0ms (3.6%)

rewrite224.0ms (4.1%)

eval2.0ms (0%)

prune4.0ms (0.1%)

regimes7.0ms (0.1%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

bsearch2.0ms (0%)

bsearch22.0ms (0.4%)

bsearch1.0ms (0%)

bsearch5.0ms (0.1%)

simplify23.0ms (0.4%)

soundness1.3s (22.9%)

preprocess162.0ms (2.9%)

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