Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

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)

sample914.0ms (20.4%)

Memory

46.5MiB live, 633.2MiB allocated; 932ms collecting garbage

Samples

665.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 253.0ms

ival-div: 138.0ms (54.5% of total)

ival-mult: 64.0ms (25.3% of total)

ival-add: 37.0ms (14.6% of total)

ival-true: 5.0ms (2% of total)

exact: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

explain97.0ms (2.2%)

Memory

-26.6MiB live, 73.5MiB allocated; 17ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
63	-	-	`(/.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	63	0
↳	`(*.f64 x x)`	overflow	63
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	63

Confusion

	Predicted +	Predicted -
+	63	0
-	0	193

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	63	0	0
-	0	0	193

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	193
1	63

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

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

ival-mult: 7.0ms (52.3% of total)

ival-div: 3.0ms (22.4% of total)

ival-add: 2.0ms (15% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess257.0ms (5.7%)

Memory

8.3MiB live, 198.3MiB allocated; 49ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	24	15
2	59	14
3	88	14
4	161	14
5	405	14
6	2753	14
7	6468	14
0	5	7
0	8	7
1	15	7
2	37	7
3	77	7
4	138	7
5	347	7
6	2391	7
7	5991	7
0	8230	6

Stop Event

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

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; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.0%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify164.0ms (3.7%)

Memory

-12.8MiB live, 136.1MiB allocated; 31ms collecting garbage

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	15	17
2	37	17
3	77	17
4	138	17
5	347	17
6	2391	17
7	5991	17
0	8230	15

Stop Event

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

Calls

Call 1

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

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

localize15.0ms (0.3%)

Memory

23.1MiB live, 23.1MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	14.722404896230547	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

10.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (39.7% of total)

ival-mult: 2.0ms (39.7% of total)

ival-add: 1.0ms (19.8% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

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))

simplify374.0ms (8.3%)

Memory

-3.6MiB live, 262.7MiB allocated; 83ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	152
1	128	150
2	362	142
3	1941	141
0	8495	135

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

rewrite405.0ms (9%)

Memory

0.5MiB live, 47.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	33	15
0	249	13

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 59

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

eval7.0ms (0.2%)

Memory: 8.9MiB live, 8.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 849 to 221 computations (74% saved)

prune4.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Accuracy

100.0%

Counts

73 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	52.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
▶	51.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	51.4%	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))

Compiler

Compiled 112 to 78 computations (30.4% saved)

simplify396.0ms (8.8%)

Memory

-25.1MiB live, 126.2MiB allocated; 15ms collecting garbage

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	107
0	30	107
1	42	107
2	81	107
3	193	107
4	458	107
5	2212	107
6	6506	107
0	8100	107

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

localize38.0ms (0.8%)

Memory

42.1MiB live, 85.0MiB allocated; 6ms collecting garbage

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.0	(-.f64 x (pow.f64 x #s(literal 3 binary64)))
accuracy	31.119263619400247	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
accuracy	0.0	(*.f64 x x)
accuracy	0.01953125	(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
accuracy	0.42057884545810226	(/.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	32.09674854905474	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
accuracy	14.722404896230547	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	30.2877279661123	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	31.379575902891176	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0.0	(fma.f64 x x #s(literal 1 binary64))
accuracy	14.722404896230547	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

28.0ms

256×

valid

Compiler

Compiled 92 to 14 computations (84.8% saved)

Precisions

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

ival-div: 6.0ms (33.5% of total)

ival-add: 4.0ms (22.3% of total)

ival-pow: 3.0ms (16.7% of total)

ival-mult: 2.0ms (11.2% of total)

ival-sub: 2.0ms (11.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series40.0ms (0.9%)

Memory

-50.2MiB live, 21.5MiB allocated; 18ms collecting garbage

Counts

14 → 25

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))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 x 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))
(*.f64 x 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 (pow x 2))
(/ 1 x)
(/ -1 (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ -1 (pow x 2))
(/ (- (pow x 2) 1) (pow x 2))
(/ 1 (pow x 2))
(pow x 3)
(pow x 2)
(/ (- 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 (/ 1 (pow x 2))))
(- 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
36.0ms	x	@	inf	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ (- 1 (/ 1 (* x x))) x) (- 1 (/ 1 (* x x))) (/ 1 (* x x)) (/ x (+ (* x x) 1)) (- x (pow x 3)) (pow x 3) (* x x))
2.0ms	x	@	-inf	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ (- 1 (/ 1 (* x x))) x) (- 1 (/ 1 (* x x))) (/ 1 (* x x)) (/ x (+ (* x x) 1)) (- x (pow x 3)) (pow x 3) (* x x))
1.0ms	x	@	0	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ (- 1 (/ 1 (* x x))) x) (- 1 (/ 1 (* x x))) (/ 1 (* x x)) (/ x (+ (* x x) 1)) (- x (pow x 3)) (pow x 3) (* x x))

Time

Variable

Point

Expression

36.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify276.0ms (6.2%)

Memory

5.7MiB live, 191.4MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	216
1	152	196
2	427	196
3	2668	196
0	8630	183

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 24

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 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ -1 (pow x 2))
(/ (- (pow x 2) 1) (pow x 2))
(/ 1 (pow x 2))
(pow x 3)
(pow x 2)
(/ (- 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 (/ 1 (pow x 2))))
(- 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))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) 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 3))
(/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ (- (pow x 2) 1) (pow x 2))
(-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 2)
(*.f64 x x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(- 1 (/ 1 (pow x 2)))
(-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(* -1 (pow x 3))
(pow.f64 (neg.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 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(neg.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))

rewrite75.0ms (1.7%)

Memory

-12.1MiB live, 34.3MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	97
0	30	97
1	97	89
0	662	89

Stop Event

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

Counts

14 → 138

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

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

eval15.0ms (0.3%)

Memory: 18.9MiB live, 18.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 708 to 566 computations (79.1% saved)

prune5.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	157	4	161

Accuracy

100.0%

Counts

161 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
✓	51.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	51.4%	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x)))

Compiler

Compiled 52 to 35 computations (32.7% saved)

simplify318.0ms (7.1%)

Memory

-19.5MiB live, 126.8MiB allocated; 19ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
0	12	31
1	23	25
2	64	25
3	142	25
4	269	25
5	588	25
6	4321	25
0	8506	24

Stop Event

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

Calls

Call 1

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

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

localize19.0ms (0.4%)

Memory

27.6MiB live, 27.6MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x (.f64 (.f64 x x) x))
accuracy	0.0	(*.f64 x x)
accuracy	0.078125	(.f64 (.f64 x x) x)
accuracy	31.119263619400247	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x)))

Samples

13.0ms

256×

valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

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

ival-mult: 3.0ms (40.7% of total)

ival-div: 2.0ms (27.1% of total)

ival-sub: 1.0ms (13.6% of total)

ival-add: 1.0ms (13.6% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms collecting garbage

Counts

4 → 16

Calls

Call 1

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

Outputs
(pow x 3)
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)
(/ 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 (/ (- (/ 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
1.0ms	x	@	-inf	((* (* x x) x) (/ x (+ (* x x) 1)) (- x (* (* x x) x)) (* x x))
1.0ms	x	@	inf	((* (* x x) x) (/ x (+ (* x x) 1)) (- x (* (* x x) x)) (* x x))
0.0ms	x	@	0	((* (* x x) x) (/ x (+ (* x x) 1)) (- x (* (* x x) x)) (* x x))

simplify485.0ms (10.8%)

Memory

-7.3MiB live, 131.8MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	171
1	133	161
2	369	161
3	1544	157
4	6745	157
0	8692	153

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 15

Calls

Call 1

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

rewrite61.0ms (1.4%)

Memory

-14.3MiB live, 36.7MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	12	24
1	52	24
0	393	23

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 45

Calls

Call 1

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

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

eval6.0ms (0.1%)

Memory: 13.9MiB live, 13.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 123 to 243 computations (78.4% saved)

prune3.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	59	4	63

Accuracy

100.0%

Counts

63 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.5%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
✓	51.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	51.4%	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x)))

Compiler

Compiled 130 to 61 computations (53.1% saved)

regimes9.0ms (0.2%)

Memory

-28.9MiB live, 16.1MiB allocated; 6ms collecting garbage

Counts

7 → 2

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
2.0ms	x

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.9%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
51.0%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
51.0%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch16.0ms (0.3%)

Memory

-12.9MiB live, 32.0MiB allocated; 2ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	1.255035775154168e-6	101464397.81163748

Samples

6.0ms

160×

valid

Compiler

Compiled 330 to 229 computations (30.6% saved)

Precisions

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

ival-div: 1.0ms (32% of total)

ival-add: 1.0ms (32% of total)

ival-mult: 1.0ms (32% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch6.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	1.255035775154168e-6	101464397.81163748

Samples

2.0ms

64×

valid

Compiler

Compiled 270 to 199 computations (26.3% saved)

Precisions

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

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

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

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

adjust: 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)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.255035775154168e-6	101464397.81163748

Compiler

Compiled 210 to 179 computations (14.8% saved)

simplify53.0ms (1.2%)

Memory

-14.9MiB live, 31.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	101
1	37	101
2	76	101
3	128	101
4	188	101
5	424	101
6	3006	101
7	7024	101

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x))) #s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Outputs
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x))) #s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (-.f64 x (.f64 (.f64 x x) x))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

derivations320.0ms (7.1%)

Memory

11.8MiB live, 203.0MiB allocated; 44ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 101 to 24 computations (76.2% saved)

preprocess92.0ms (2%)

Memory: 2.3MiB live, 95.3MiB allocated; 38ms collecting garbage
Compiler: Compiled 302 to 100 computations (66.9% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample914.0ms (20.4%)

explain97.0ms (2.2%)

preprocess257.0ms (5.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify164.0ms (3.7%)

localize15.0ms (0.3%)

series2.0ms (0%)

simplify374.0ms (8.3%)

rewrite405.0ms (9%)

eval7.0ms (0.2%)

prune4.0ms (0.1%)

simplify396.0ms (8.8%)

localize38.0ms (0.8%)

series40.0ms (0.9%)

simplify276.0ms (6.2%)

rewrite75.0ms (1.7%)

eval15.0ms (0.3%)

prune5.0ms (0.1%)

simplify318.0ms (7.1%)

localize19.0ms (0.4%)

series3.0ms (0.1%)

simplify485.0ms (10.8%)

rewrite61.0ms (1.4%)

eval6.0ms (0.1%)

prune3.0ms (0.1%)

regimes9.0ms (0.2%)

regimes2.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch16.0ms (0.3%)

bsearch6.0ms (0.1%)

bsearch1.0ms (0%)

simplify53.0ms (1.2%)

derivations320.0ms (7.1%)

preprocess92.0ms (2%)

end0.0ms (0%)

Profiling