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

0.5MiB live, 0.5MiB 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)

sample783.0ms (33.9%)

Memory

33.4MiB live, 810.8MiB allocated

Samples

525.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 387.0ms

ival-mult: 318.0ms (82.3% of total)

ival-sub: 51.0ms (13.2% of total)

exact: 8.0ms (2.1% of total)

ival-true: 6.0ms (1.6% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain82.0ms (3.6%)

Memory

-6.0MiB live, 111.8MiB 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

30.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 16.0ms (83.2% of total)

ival-sub: 3.0ms (15.6% of total)

exact: 1.0ms (5.2% of total)

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

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

preprocess21.0ms (0.9%)

Memory

-3.3MiB live, 32.1MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.3MiB 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

5.7MiB live, 5.6MiB 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)

localize18.0ms (0.8%)

Memory

-2.6MiB live, 35.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 2 binary64))

Samples

13.0ms

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 (59.2% of total)

ival-sub: 1.0ms (19.7% 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

6.9MiB live, 6.9MiB 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))

simplify96.0ms (4.1%)

Memory

-20.9MiB live, 114.9MiB 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)

rewrite179.0ms (7.8%)

Memory

29.5MiB live, 187.5MiB 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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eval92.0ms (4%)

Memory: -12.3MiB live, 61.6MiB allocated
Compiler: Compiled 7 299 to 642 computations (91.2% saved)

prune4.0ms (0.2%)

Memory

17.1MiB live, 17.1MiB 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 x x) #s(literal 2 binary64) #s(literal -1 binary64))
▶	54.5%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	46.0%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify83.0ms (3.6%)

Memory

-44.2MiB live, 3.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
cost-diff	0	(*.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	12	45
0	15	43
1	22	43
2	25	43
0	25	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 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#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 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)

localize20.0ms (0.9%)

Memory

26.0MiB live, 26.0MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	29.122978898612224	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	34.53240702434802	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Samples

13.0ms

256×

valid

Compiler

Compiled 40 to 10 computations (75% saved)

Precisions

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

ival-mult: 3.0ms (47.1% of total)

ival-sub: 1.0ms (15.7% of total)

ival-add: 1.0ms (15.7% 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

2.8MiB live, 2.8MiB allocated

Counts

5 → 60

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((- (* (* x x) 2) 1) (- (* (* x x) 2) 1) (* (* x x) 2) (* x x) (+ (* (* x x) 2) -1))
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) (- (* (* x x) 2) 1) (* (* x x) 2) (* x x) (+ (* (* x x) 2) -1))
0.0ms	x	@	0	((- (* (* x x) 2) 1) (- (* (* x x) 2) 1) (* (* x x) 2) (* x x) (+ (* (* x x) 2) -1))

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

simplify86.0ms (3.7%)

Memory

-0.1MiB live, 75.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	318
1	19	318
2	40	318
3	85	318
4	201	318
5	342	318
6	835	318
7	2313	318
8	3232	318
9	5538	318
0	8305	291

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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 (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 (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))))

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 (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 (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))

rewrite200.0ms (8.7%)

Memory

15.6MiB live, 206.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
0	15	34
1	45	34
2	249	34
3	2365	34
0	9306	34

Stop Event

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

Counts

5 → 288

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

Outputs
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eval121.0ms (5.2%)

Memory: -11.2MiB live, 113.2MiB allocated
Compiler: Compiled 7 217 to 737 computations (89.8% saved)

prune12.0ms (0.5%)

Memory

-7.1MiB live, 30.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	370	3	373

Accuracy

100.0%

Counts

373 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
✓	54.5%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	46.0%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 35 to 23 computations (34.3% saved)

regimes8.0ms (0.3%)

Memory

17.6MiB live, 17.6MiB 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 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

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

regimes12.0ms (0.5%)

Memory

-29.5MiB live, 12.8MiB 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:

7.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
2.0ms	x
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
98.8%	2	`x`
98.8%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
98.8%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
98.8%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB 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
46.0%	1	`x`
46.0%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
46.0%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
46.0%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch11.0ms (0.5%)

Memory

18.8MiB live, 18.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	8.475633018351266e-7	10.96633595230892

Samples

4.0ms

144×

valid

Compiler

Compiled 64 to 91 computations (-42.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-sub: 1.0ms (51.3% of total)

ival-mult: 1.0ms (51.3% of total)

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

exact: 0.0ms (0% of total)

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

simplify26.0ms (1.1%)

Memory

-20.7MiB live, 54.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	19	43

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

soundness370.0ms (16%)

Memory

16.3MiB live, 252.6MiB 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
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×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 42 to 27 computations (35.7% saved)

preprocess69.0ms (3%)

Memory: 16.6MiB live, 54.4MiB allocated
Remove: (abs x)
Compiler: Compiled 70 to 44 computations (37.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample783.0ms (33.9%)

explain82.0ms (3.6%)

preprocess21.0ms (0.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize18.0ms (0.8%)

series3.0ms (0.1%)

simplify96.0ms (4.1%)

rewrite179.0ms (7.8%)

eval92.0ms (4%)

prune4.0ms (0.2%)

simplify83.0ms (3.6%)

localize20.0ms (0.9%)

series3.0ms (0.1%)

simplify86.0ms (3.7%)

rewrite200.0ms (8.7%)

eval121.0ms (5.2%)

prune12.0ms (0.5%)

regimes8.0ms (0.3%)

regimes12.0ms (0.5%)

regimes5.0ms (0.2%)

bsearch11.0ms (0.5%)

simplify26.0ms (1.1%)

soundness370.0ms (16%)

preprocess69.0ms (3%)

end0.0ms (0%)

Profiling