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

0.2MiB live, 0.2MiB 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)

sample622.0ms (22.4%)

Memory

0.3MiB live, 787.3MiB allocated

Samples

325.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 203.0ms

ival-mult: 110.0ms (54.2% of total)

ival-sub: 77.0ms (37.9% of total)

exact: 8.0ms (3.9% of total)

ival-true: 5.0ms (2.5% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain62.0ms (2.2%)

Memory

33.2MiB live, 110.9MiB 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 48 to 22 computations (54.2% saved)

Precisions

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

ival-mult: 7.0ms (69.9% of total)

ival-sub: 2.0ms (20% of total)

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

exact: 0.0ms (0% of total)

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

preprocess87.0ms (3.1%)

Memory

-13.9MiB live, 25.0MiB 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 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))

Symmetry

(abs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB 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 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB 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 (*.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)

localize19.0ms (0.7%)

Memory

-14.9MiB live, 30.9MiB 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	0.01171875	(.f64 (.f64 x x) #s(literal 2 binary64))

Samples

12.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sub: 3.0ms (44.4% of total)

ival-mult: 3.0ms (44.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB 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 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 (.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 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 (* 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 (* 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 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 (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 (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

9 calls:

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

simplify336.0ms (12.1%)

Memory

16.1MiB live, 129.5MiB 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))
(* (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))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (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)
(pow x 2)
(pow x 2)
(pow x 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 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* 2 (pow x 2)) 1)
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* 2 (pow x 2)) 1)
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite405.0ms (14.6%)

Memory

-16.3MiB live, 429.4MiB 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
(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (fma.f64 (.f64 x x) #s(literal -2 binary64) #s(literal -1 binary64))))
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(.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 64 binary64) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))))))))
(.f64 (-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) (.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)) (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64)))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))))))
(.f64 (-.f64 (.f64 #s(literal 64 binary64) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))))))
(.f64 (fma.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 x (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64))) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 512 binary64)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64))) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64))) #s(literal -1 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64))) (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 4 binary64) #s(literal -2 binary64)) #s(literal -1 binary64)))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 4 binary64) #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 4 binary64) #s(literal -2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -4 binary64) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64))) (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 512 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 2 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (log.f64 (.f64 (.f64 x x) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.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))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(.f64 x (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 x (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))) x)
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (.f64 x x))
(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))

eval40.0ms (1.4%)

Memory: 19.2MiB live, 56.1MiB allocated
Compiler: Compiled 12 525 to 640 computations (94.9% saved)

prune54.0ms (1.9%)

Memory

-6.4MiB live, 78.9MiB 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))
▶	50.0%	#s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	49.4%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify6.0ms (0.2%)

Memory

-30.5MiB live, 7.7MiB 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 #s(literal 2 binary64) (.f64 x x))
cost-diff	0	#s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x)))
cost-diff	0	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
0	16	43
1	25	43
2	27	43
0	27	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 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x
(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 #s(literal 2 binary64) (.f64 x x)))
#s(approx (- (* (* x x) 2) 1) (.f64 x (.f64 x #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 x (.f64 x #s(literal 2 binary64)))
#s(literal 2 binary64)
(*.f64 x x)
x
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 x (*.f64 x #s(literal 2 binary64)) #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)

localize28.0ms (1%)

Memory

17.0MiB live, 52.4MiB 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	0.01171875	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	31.982376008711615	#s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x)))
accuracy	32.36295422964362	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Samples

18.0ms

256×

valid

Compiler

Compiled 40 to 11 computations (72.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 5.0ms (65.6% of total)

ival-sub: 1.0ms (13.1% of total)

ival-add: 1.0ms (13.1% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB 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 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<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 (* 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) #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 -1 (taylor 0 x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (pow x 2)) 1) (taylor 0 x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (pow x 2)) 1) (taylor 0 x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (pow x 2)) 1) (taylor 0 x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 2 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) (patch #s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.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 (pow x 2) (taylor 0 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 (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 (pow x 2) (taylor -inf 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 (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 (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

15 calls:

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

simplify151.0ms (5.4%)

Memory

-4.3MiB live, 228.0MiB 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)
(* 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))))
-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))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (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)
(pow x 2)
(pow x 2)
(pow x 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))))

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

rewrite257.0ms (9.3%)

Memory

27.1MiB live, 392.4MiB allocated

Rules

8 820×	`lower-fma.f32`
8 818×	`lower-fma.f64`
3 542×	`lower-*.f32`
3 538×	`lower-*.f64`
2 852×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
0	16	34
1	48	34
2	269	34
3	2472	34
0	8957	34

Stop Event

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

Counts

5 → 287

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 x (.f64 x #s(literal 2 binary64))))
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(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64)))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -4 binary64) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 #s(literal 16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 512 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) #s(literal 1 binary64))))

eval48.0ms (1.7%)

Memory: -28.9MiB live, 86.6MiB allocated
Compiler: Compiled 10 530 to 663 computations (93.7% saved)

prune134.0ms (4.8%)

Memory

16.4MiB live, 93.2MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	367	3	370

Accuracy

100.0%

Counts

370 → 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))
✓	50.0%	#s(approx (- (* (* x x) 2) 1) (.f64 #s(literal 2 binary64) (.f64 x x)))
✓	49.4%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 39 to 20 computations (48.7% saved)

regimes8.0ms (0.3%)

Memory

13.7MiB live, 13.7MiB 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 #s(literal 2 binary64) (.f64 x x)))
(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 x 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 20 to 13 computations (35% saved)

regimes8.0ms (0.3%)

Memory

-34.0MiB live, 13.8MiB 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 #s(literal 2 binary64) (.f64 x x)))

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

Calls

4 calls:

3.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
97.7%	2	`x`
97.7%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
97.7%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
97.7%	2	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes5.0ms (0.2%)

Memory

11.1MiB live, 11.1MiB 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
49.4%	1	`x`
49.4%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
49.4%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
49.4%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

bsearch8.0ms (0.3%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	0.02436655591115789	3.7667174534052186

Samples

3.0ms

112×

valid

Compiler

Compiled 81 to 59 computations (27.2% saved)

Precisions

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

ival-mult: 1.0ms (73.3% 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)

simplify7.0ms (0.2%)

Memory

-25.5MiB live, 13.3MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

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

#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 #s(literal 2 binary64) (.f64 x x))))
(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))

soundness439.0ms (15.8%)

Memory

12.3MiB live, 220.4MiB 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 47 to 25 computations (46.8% saved)

preprocess50.0ms (1.8%)

Memory: 3.4MiB live, 38.9MiB allocated
Remove: (abs x)
Compiler: Compiled 76 to 40 computations (47.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample622.0ms (22.4%)

explain62.0ms (2.2%)

preprocess87.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize19.0ms (0.7%)

series2.0ms (0.1%)

simplify336.0ms (12.1%)

rewrite405.0ms (14.6%)

eval40.0ms (1.4%)

prune54.0ms (1.9%)

simplify6.0ms (0.2%)

localize28.0ms (1%)

series2.0ms (0.1%)

simplify151.0ms (5.4%)

rewrite257.0ms (9.3%)

eval48.0ms (1.7%)

prune134.0ms (4.8%)

regimes8.0ms (0.3%)

regimes8.0ms (0.3%)

regimes5.0ms (0.2%)

bsearch8.0ms (0.3%)

simplify7.0ms (0.2%)

soundness439.0ms (15.8%)

preprocess50.0ms (1.8%)

end0.0ms (0%)

Profiling