Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample735.0ms (31.9%)

Memory

55.1MiB live, 950.5MiB allocated

Samples

391.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 243.0ms

ival-mult: 160.0ms (65.8% of total)

ival-sub: 65.0ms (26.7% of total)

exact: 9.0ms (3.7% of total)

ival-true: 6.0ms (2.5% of total)

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

Bogosity

explain82.0ms (3.5%)

Memory

1.9MiB live, 75.9MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`#s(literal 1 binary64)`
-	-	`(.f64 (.f64 x x) #s(literal 2 binary64))`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

29.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-mult: 7.0ms (65.5% of total)

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

exact: 1.0ms (9.4% of total)

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

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

preprocess20.0ms (0.9%)

Memory

-20.5MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	25	15
2	72	14
3	178	14
4	255	14
5	280	14
6	284	14
0	6	7
0	9	7
1	17	7
2	21	7
0	21	6

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

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

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
cost-diff	128	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	17	18
2	21	18
0	21	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)

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

localize33.0ms (1.4%)

Memory

-43.5MiB live, 25.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	0.01171875	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 3.0ms (57.7% of total)

ival-sub: 1.0ms (19.2% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

#s(alt (-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (patch (-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())

#s(alt (*.f64 (*.f64 x x) #s(literal 2 binary64)) (patch (*.f64 (*.f64 x x) #s(literal 2 binary64)) #<representation binary64>) () ())

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

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

Calls

3 calls:

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

simplify97.0ms (4.2%)

Memory

17.9MiB live, 89.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	170
1	19	170
2	40	170
3	85	170
4	201	170
5	342	170
6	835	170
7	2313	170
8	3232	170
9	5538	170
0	8305	161

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

rewrite183.0ms (8%)

Memory

8.0MiB live, 248.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	31	15
2	173	15
3	1563	15
0	8539	14

Stop Event

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

Counts

3 → 244

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)

Outputs
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eval33.0ms (1.5%)

Memory: 0.5MiB live, 74.4MiB allocated
Compiler: Compiled 7 299 to 642 computations (91.2% saved)

prune4.0ms (0.2%)

Memory

17.5MiB live, 17.5MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	277	3	280
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	3	281

Accuracy

100.0%

Counts

281 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
▶	53.5%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	46.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify3.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
0	18	43
1	28	43
0	28	43

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize30.0ms (1.3%)

Memory

-37.9MiB live, 43.7MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	29.776504920593407	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	34.00455248045505	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Samples

18.0ms

256×

valid

Compiler

Compiled 40 to 12 computations (70% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 6.0ms (66.1% of total)

ival-sub: 1.0ms (11% of total)

ival-add: 1.0ms (11% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify91.0ms (4%)

Memory

5.8MiB live, 113.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	354
1	21	354
2	40	354
3	82	354
4	199	354
5	342	354
6	759	354
7	2153	354
8	3079	354
9	5377	354
0	8163	327

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

rewrite446.0ms (19.4%)

Memory

-96.8MiB live, 224.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
0	18	37
1	59	37
2	270	37
3	2487	37
0	8999	37

Stop Event

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

Counts

6 → 291

Calls

Call 1

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

Outputs
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eval50.0ms (2.2%)

Memory: -26.1MiB live, 133.5MiB allocated
Compiler: Compiled 7 145 to 717 computations (90% saved)

prune11.0ms (0.5%)

Memory

4.9MiB live, 44.2MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	363	3	366

Accuracy

100.0%

Counts

366 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
✓	53.5%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	46.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 35 to 24 computations (31.4% saved)

regimes8.0ms (0.4%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(*.f64 x x)
2.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes9.0ms (0.4%)

Memory

-21.8MiB live, 16.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.2%)

Memory

10.7MiB live, 10.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(*.f64 x x)
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
46.9%	1	`x`
46.9%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
46.9%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
46.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch8.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	0.10667516486090742	0.8818876715182359

Samples

3.0ms

96×

valid

Compiler

Compiled 46 to 64 computations (-39.1% saved)

Precisions

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

ival-mult: 1.0ms (77.8% of total)

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

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

exact: 0.0ms (0% of total)

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

simplify69.0ms (3%)

Memory

-0.8MiB live, 37.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	21	43

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

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

soundness345.0ms (15%)

Memory

-23.6MiB live, 196.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	170
1	19	170
2	40	170
3	85	170
4	201	170
5	342	170
6	835	170
7	2313	170
8	3232	170
9	5538	170
0	8305	161
0	6	15
0	9	15
1	31	15
2	173	15
3	1563	15
0	8539	14

Stop Event

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

Compiler

Compiled 42 to 29 computations (31% saved)

preprocess28.0ms (1.2%)

Memory: -9.3MiB live, 67.6MiB allocated
Remove: (abs x)
Compiler: Compiled 82 to 56 computations (31.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample735.0ms (31.9%)

explain82.0ms (3.5%)

preprocess20.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize33.0ms (1.4%)

series3.0ms (0.1%)

simplify97.0ms (4.2%)

rewrite183.0ms (8%)

eval33.0ms (1.5%)

prune4.0ms (0.2%)

simplify3.0ms (0.1%)

localize30.0ms (1.3%)

series4.0ms (0.2%)

simplify91.0ms (4%)

rewrite446.0ms (19.4%)

eval50.0ms (2.2%)

prune11.0ms (0.5%)

regimes8.0ms (0.4%)

regimes9.0ms (0.4%)

regimes5.0ms (0.2%)

bsearch8.0ms (0.3%)

simplify69.0ms (3%)

soundness345.0ms (15%)

preprocess28.0ms (1.2%)

end0.0ms (0%)

Profiling