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

0.3MiB live, 0.3MiB 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)

sample957.0ms (37.3%)

Memory

19.8MiB live, 645.6MiB allocated

Samples

513.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 250.0ms

ival-mult: 153.0ms (61.2% of total)

ival-sub: 80.0ms (32% of total)

exact: 8.0ms (3.2% of total)

ival-true: 6.0ms (2.4% of total)

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

Bogosity

explain102.0ms (4%)

Memory

-23.1MiB live, 135.9MiB 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

21.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-mult: 7.0ms (68.9% of total)

ival-sub: 2.0ms (19.7% of total)

exact: 1.0ms (9.8% of total)

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

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

preprocess16.0ms (0.6%)

Memory

33.7MiB live, 33.7MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`associate-r`
36×	`distribute-lft-neg-in`
30×	`associate-l`
28×	`distribute-rgt-neg-in`
24×	`distribute-lft-in`

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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify43.0ms (1.7%)

Memory

-32.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

14×	`lower-*.f32`
10×	`lower-*.f64`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
6×	`*-commutative`

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)

localize16.0ms (0.6%)

Memory

31.7MiB live, 31.7MiB 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	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 3.0ms (52.6% of total)

ival-sub: 2.0ms (35.1% of total)

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

exact: 0.0ms (0% of total)

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

series70.0ms (2.7%)

Memory

-29.9MiB live, 7.4MiB 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))

simplify162.0ms (6.3%)

Memory

14.4MiB live, 113.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4 322×	`lower-*.f64`
4 322×	`lower-*.f32`
2 742×	`lower-fma.f64`
2 742×	`lower-fma.f32`
1 600×	`div-sub`

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)

rewrite187.0ms (7.3%)

Memory

3.1MiB live, 348.9MiB allocated

Rules

12 208×	`lower-fma.f64`
12 208×	`lower-fma.f32`
3 996×	`lower-*.f32`
3 992×	`lower-*.f64`
3 976×	`lower-/.f64`

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 (3.6%)

Memory: -21.7MiB live, 102.1MiB allocated
Compiler: Compiled 7 299 to 642 computations (91.2% saved)

prune5.0ms (0.2%)

Memory

17.6MiB 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 x x) #s(literal 2 binary64) #s(literal -1 binary64))
▶	46.0%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	53.7%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify4.0ms (0.2%)

Memory

5.4MiB live, 5.4MiB 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))

Rules

14×	`lower-*.f32`
10×	`lower-*.f64`
8×	`lower-fma.f32`
6×	`*-commutative`
6×	`lower-fma.f64`

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)

localize30.0ms (1.2%)

Memory

2.6MiB live, 40.5MiB 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	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	34.582528324185496	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	29.65032844680504	#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 (48.6% of total)

ival-sub: 1.0ms (16.2% of total)

ival-add: 1.0ms (16.2% 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

6.5MiB live, 6.5MiB 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

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))

simplify124.0ms (4.8%)

Memory

-29.4MiB live, 151.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4 322×	`lower-*.f64`
4 322×	`lower-*.f32`
2 742×	`lower-fma.f64`
2 742×	`lower-fma.f32`
1 600×	`div-sub`

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))

rewrite169.0ms (6.6%)

Memory

2.8MiB live, 278.6MiB allocated

Rules

10 184×	`lower-fma.f32`
10 182×	`lower-fma.f64`
3 586×	`lower-*.f32`
3 582×	`lower-*.f64`
2 994×	`lower-/.f64`

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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eval59.0ms (2.3%)

Memory: 19.0MiB live, 95.6MiB allocated
Compiler: Compiled 7 217 to 737 computations (89.8% saved)

prune38.0ms (1.5%)

Memory

-6.6MiB live, 38.9MiB 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))
✓	46.0%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	53.7%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 35 to 23 computations (34.3% saved)

regimes10.0ms (0.4%)

Memory

-12.0MiB live, 25.3MiB 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:

4.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
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)

regimes8.0ms (0.3%)

Memory

-16.0MiB live, 21.8MiB 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:

3.0ms	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))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
97.8%	2	`x`
97.8%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
97.8%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
97.8%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.2%)

Memory

15.3MiB live, 15.3MiB 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
53.7%	1	`x`
53.7%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
53.7%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
53.7%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch12.0ms (0.5%)

Memory

-16.6MiB live, 21.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.11284686238773584	31356.306601387903

Samples

5.0ms

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 (48.9% of total)

ival-mult: 1.0ms (48.9% of total)

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

exact: 0.0ms (0% of total)

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

simplify53.0ms (2.1%)

Memory

29.9MiB live, 76.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`1-exp-binary32-exp.f32`
2×	`-commutative-binary64-.f64`
2×	`1-exp-binary64-exp.f64`

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))

soundness355.0ms (13.8%)

Memory

-22.0MiB live, 208.5MiB allocated

Rules

12 208×	`lower-fma.f64`
12 208×	`lower-fma.f32`
4 322×	`lower-*.f64`
4 322×	`lower-*.f32`
3 996×	`lower-*.f32`

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 27 computations (35.7% saved)

preprocess45.0ms (1.8%)

Memory: 11.6MiB live, 98.8MiB 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%)

sample957.0ms (37.3%)

explain102.0ms (4%)

preprocess16.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify43.0ms (1.7%)

localize16.0ms (0.6%)

series70.0ms (2.7%)

simplify162.0ms (6.3%)

rewrite187.0ms (7.3%)

eval92.0ms (3.6%)

prune5.0ms (0.2%)

simplify4.0ms (0.2%)

localize30.0ms (1.2%)

series3.0ms (0.1%)

simplify124.0ms (4.8%)

rewrite169.0ms (6.6%)

eval59.0ms (2.3%)

prune38.0ms (1.5%)

regimes10.0ms (0.4%)

regimes8.0ms (0.3%)

regimes5.0ms (0.2%)

bsearch12.0ms (0.5%)

simplify53.0ms (2.1%)

soundness355.0ms (13.8%)

preprocess45.0ms (1.8%)

end0.0ms (0%)

Profiling