Metrics for Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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 7 to 6 computations (14.3% saved)

sample461.0ms (16.4%)

Memory

-13.5MiB live, 545.5MiB allocated

Samples

274.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-mult: 78.0ms (55.9% of total)

ival-add: 47.0ms (33.7% of total)

ival-true: 5.0ms (3.6% of total)

exact: 5.0ms (3.6% of total)

ival-assert: 4.0ms (2.9% of total)

Bogosity

explain47.0ms (1.7%)

Memory

34.1MiB live, 72.1MiB allocated

FPErrors

Click to see full error table

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

19.0ms

512×

valid

Compiler

Compiled 39 to 20 computations (48.7% saved)

Precisions

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

ival-mult: 4.0ms (51.4% of total)

ival-add: 3.0ms (38.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess15.0ms (0.5%)

Memory

-19.0MiB live, 18.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	22	10
2	54	10
3	98	10
4	133	10
5	147	10
6	149	10
0	4	5
0	6	5
1	9	5
0	9	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify2.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	9	10
0	9	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (0.5%)

Memory

-13.2MiB live, 23.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)

Samples

8.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (56.4% of total)

ival-add: 1.0ms (28.2% 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

5.1MiB live, 5.1MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 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 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 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 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 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 (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 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) 1) (* x x))
0.0ms	x	@	-inf	((+ (* x x) 1) (* x x))
0.0ms	x	@	0	((+ (* x x) 1) (* x x))

simplify263.0ms (9.4%)

Memory

32.2MiB live, 297.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	88
1	20	88
2	35	88
3	56	88
4	88	88
5	102	88
6	131	88
7	224	88
8	585	88
9	1594	88
10	3141	88
11	4984	88
12	5390	88
13	5742	88
14	6103	88
15	6286	88
0	8901	79

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

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

rewrite440.0ms (15.7%)

Memory

-11.8MiB live, 257.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	24	8
2	145	8
3	1172	8
0	8447	7

Stop Event

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

Counts

2 → 281

Calls

Call 1

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

Outputs
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eval74.0ms (2.6%)

Memory: -19.3MiB live, 56.0MiB allocated
Compiler: Compiled 7 005 to 638 computations (90.9% saved)

prune5.0ms (0.2%)

Memory

15.7MiB live, 15.7MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	302	3	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	303	3	306

Accuracy

100.0%

Counts

306 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x #s(literal 1 binary64))
▶	49.9%	#s(approx (+ (* x x) 1) (*.f64 x x))
▶	54.0%	#s(approx (+ (* x x) 1) #s(literal 1 binary64))

Compiler

Compiled 10 to 9 computations (10% saved)

simplify3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	9	25
1	12	25
0	12	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize33.0ms (1.2%)

Memory

-23.6MiB live, 15.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	32.081629700301036	#s(approx (+ (* x x) 1) (*.f64 x x))
accuracy	29.449538241218733	#s(approx (+ (* x x) 1) #s(literal 1 binary64))

Samples

29.0ms

256×

valid

Compiler

Compiled 41 to 12 computations (70.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (54.6% of total)

ival-add: 1.0ms (27.3% 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

2.4MiB live, 2.4MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

simplify302.0ms (10.8%)

Memory

29.6MiB live, 225.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	192
1	20	192
2	35	192
3	56	192
4	88	192
5	102	192
6	131	192
7	224	192
8	585	192
9	1594	192
10	3141	192
11	4984	192
12	5390	192
13	5742	192
14	6103	192
15	6286	192
0	8901	165

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite333.0ms (11.9%)

Memory

-29.8MiB live, 289.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
0	9	21
1	27	21
2	148	21
3	1177	21
0	8515	21

Stop Event

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

Counts

4 → 268

Calls

Call 1

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

Outputs
#<batchref>
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eval83.0ms (3%)

Memory: 8.2MiB live, 82.4MiB allocated
Compiler: Compiled 6 757 to 617 computations (90.9% saved)

prune6.0ms (0.2%)

Memory

19.5MiB live, 19.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	316	3	319

Accuracy

100.0%

Counts

319 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	49.9%	#s(approx (+ (* x x) 1) (*.f64 x x))
✓	54.0%	#s(approx (+ (* x x) 1) #s(literal 1 binary64))

Compiler

Compiled 25 to 16 computations (36% saved)

regimes6.0ms (0.2%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes6.0ms (0.2%)

Memory

-27.4MiB live, 9.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	2	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
99.7%	2	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
54.0%	1	`x`
54.0%	1	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
54.0%	1	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch11.0ms (0.4%)

Memory

18.5MiB live, 18.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	1.2110309678375067e-5	480517185094579.2

Samples

4.0ms

176×

valid

Compiler

Compiled 52 to 85 computations (-63.5% saved)

Precisions

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

ival-add: 1.0ms (84.6% of total)

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

exact: 0.0ms (0% of total)

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

simplify12.0ms (0.4%)

Memory

-36.4MiB live, 9.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	13	33

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 x x #s(literal 1 binary64))

(if (<=.f64 (*.f64 x x) #s(literal 1 binary64)) #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #s(approx (+ (* x x) 1) (*.f64 x x)))

#s(approx (+ (* x x) 1) #s(literal 1 binary64))

Outputs

(fma.f64 x x #s(literal 1 binary64))

(if (<=.f64 (*.f64 x x) #s(literal 1 binary64)) #s(approx (+ (* x x) 1) #s(literal 1 binary64)) #s(approx (+ (* x x) 1) (*.f64 x x)))

#s(approx (+ (* x x) 1) #s(literal 1 binary64))

soundness584.0ms (20.8%)

Memory

33.3MiB live, 300.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	24	8
2	145	8
3	1172	8
0	8447	7
0	8	88
1	20	88
2	35	88
3	56	88
4	88	88
5	102	88
6	131	88
7	224	88
8	585	88
9	1594	88
10	3141	88
11	4984	88
12	5390	88
13	5742	88
14	6103	88
15	6286	88
0	8901	79

Stop Event

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

Compiler

Compiled 32 to 19 computations (40.6% saved)

preprocess93.0ms (3.3%)

Memory: -45.4MiB live, 52.8MiB allocated
Remove: (abs x)
Compiler: Compiled 54 to 30 computations (44.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample461.0ms (16.4%)

explain47.0ms (1.7%)

preprocess15.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0.1%)

localize15.0ms (0.5%)

series3.0ms (0.1%)

simplify263.0ms (9.4%)

rewrite440.0ms (15.7%)

eval74.0ms (2.6%)

prune5.0ms (0.2%)

simplify3.0ms (0.1%)

localize33.0ms (1.2%)

series2.0ms (0.1%)

simplify302.0ms (10.8%)

rewrite333.0ms (11.9%)

eval83.0ms (3%)

prune6.0ms (0.2%)

regimes6.0ms (0.2%)

regimes6.0ms (0.2%)

regimes4.0ms (0.1%)

bsearch11.0ms (0.4%)

simplify12.0ms (0.4%)

soundness584.0ms (20.8%)

preprocess93.0ms (3.3%)

end0.0ms (0%)

Profiling