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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

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)

sample797.0ms (30.6%)

Memory

62.1MiB live, 1 050.4MiB allocated; 198ms collecting garbage

Samples

514.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 295.0ms

ival-mult: 176.0ms (59.6% of total)

ival-sub: 102.0ms (34.5% of total)

exact: 8.0ms (2.7% of total)

ival-true: 4.0ms (1.4% of total)

ival-assert: 3.0ms (1% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

explain137.0ms (5.2%)

Memory

-11.3MiB live, 132.3MiB allocated; 19ms collecting garbage

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

54.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 39.0ms (92% of total)

ival-sub: 2.0ms (4.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess181.0ms (7%)

Memory

-11.0MiB live, 189.8MiB allocated; 63ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	23	15
2	73	15
3	212	15
4	710	14
5	3488	14
0	6	7
0	9	7
1	19	7
2	56	7
3	202	7
4	660	7
5	4036	7
0	8535	6

Stop Event

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

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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

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)

simplify112.0ms (4.3%)

Memory

5.0MiB live, 140.3MiB allocated; 20ms collecting garbage

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	19	18
2	56	18
3	202	18
4	660	18
5	4036	18
0	8535	17

Stop Event

1×	iter limit
1×	node limit
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)

localize32.0ms (1.2%)

Memory

-1.6MiB live, 54.1MiB allocated; 10ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))

Samples

27.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 8.0ms (81% of total)

ival-sub: 1.0ms (10.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Counts

3 → 5

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

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))

simplify140.0ms (5.4%)

Memory

3.0MiB live, 137.6MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	17	27
2	49	27
3	177	27
4	899	27
5	7159	27
0	8159	26

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 5

Calls

Call 1

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

rewrite50.0ms (1.9%)

Memory

7.3MiB live, 60.9MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	34	15
0	234	14

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 60

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 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.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 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 x (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 3 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)))))
(-.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 x x)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(.f64 x (.f64 #s(literal 2 binary64) x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) x (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 x x (*.f64 x x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval15.0ms (0.6%)

Memory: -21.2MiB live, 23.0MiB allocated; 11ms collecting garbage
Compiler: Compiled 693 to 168 computations (75.8% saved)

prune2.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	2	66

Accuracy

100.0%

Counts

66 → 2

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))
▶	51.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify193.0ms (7.4%)

Memory

14.4MiB live, 152.7MiB allocated; 41ms collecting garbage

Localize:

Found 3 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	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	22
0	13	22
1	24	22
2	70	22
3	267	21
4	846	21
5	3827	21
0	8171	21

Stop Event

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

Calls

Call 1

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

localize35.0ms (1.3%)

Memory

5.5MiB live, 51.0MiB allocated; 4ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	30.787114968231343	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Samples

29.0ms

256×

valid

Compiler

Compiled 23 to 10 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-sub: 18.0ms (77.9% of total)

ival-mult: 3.0ms (13% of total)

ival-add: 1.0ms (4.3% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series1.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Counts

3 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

simplify228.0ms (8.7%)

Memory

-41.4MiB live, 157.5MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	17	27
2	49	27
3	177	27
4	899	27
5	7152	27
0	8152	26

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 5

Calls

Call 1

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

rewrite45.0ms (1.7%)

Memory

44.3MiB live, 135.4MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
0	13	18
1	48	17
0	336	17

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 46

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64))) (neg.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal -2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal -2 binary64))))
(fma.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 x (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 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 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal 2 binary64)))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (.f64 x x)))
(-.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) (.f64 #s(literal 2 binary64) x)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #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))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval14.0ms (0.6%)

Memory: -18.8MiB live, 31.6MiB allocated; 9ms collecting garbage
Compiler: Compiled 602 to 128 computations (78.7% saved)

prune2.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	49	3	52

Accuracy

100.0%

Counts

52 → 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))
▶	48.9%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	51.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify123.0ms (4.7%)

Memory

-32.1MiB live, 157.6MiB allocated; 21ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
0	11	23
1	21	23
2	58	23
3	204	23
4	666	23
5	4045	23
0	8548	22

Stop Event

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

Calls

Call 1

Inputs
#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)

Outputs
#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)

localize21.0ms (0.8%)

Memory

30.0MiB live, 30.0MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	32.6841387359206	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))

Samples

10.0ms

256×

valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

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

ival-mult: 3.0ms (62.3% of total)

ival-sub: 1.0ms (20.8% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated; 0ms collecting garbage

Counts

3 → 5

Calls

Call 1

Inputs
#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)

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

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))
0.0ms	x	@	0	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))

simplify205.0ms (7.9%)

Memory

8.2MiB live, 140.0MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	17	27
2	49	27
3	177	27
4	899	27
5	7152	27
0	8152	26

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 5

Calls

Call 1

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

rewrite46.0ms (1.8%)

Memory

-20.7MiB live, 76.0MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
0	11	21
1	36	21
0	236	20

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 41

Calls

Call 1

Inputs
#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)

Outputs
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 x (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(.f64 x (.f64 #s(literal 2 binary64) x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) x (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x (*.f64 x x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval5.0ms (0.2%)

Memory: 15.1MiB live, 15.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 712 to 133 computations (81.3% saved)

prune3.0ms (0.1%)

Memory

10.5MiB live, 10.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	46	3	49

Accuracy

100.0%

Counts

49 → 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))
✓	48.9%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	51.9%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes9.0ms (0.4%)

Memory

-24.0MiB live, 20.6MiB allocated; 6ms collecting garbage

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

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

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:

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

Results

Accuracy	Segments	Branch
99.0%	2	`(*.f64 x x)`
99.0%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
99.0%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
99.0%	2	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes4.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

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
51.9%	1	`(*.f64 x x)`
51.9%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
51.9%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
51.9%	1	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch17.0ms (0.6%)

Memory

-1.1MiB live, 41.4MiB allocated; 8ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.06680421396527143	994233.8036139732

Samples

10.0ms

144×

valid

Compiler

Compiled 208 to 190 computations (8.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (72.3% of total)

ival-sub: 1.0ms (36.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

simplify81.0ms (3.1%)

Memory

-49.9MiB live, 81.4MiB allocated; 66ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	25	41
2	62	41
3	217	41
4	1093	41
5	4457	41

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal 3152519739159347/4503599627370496 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 x #s(literal 3152519739159347/4503599627370496 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))

derivations68.0ms (2.6%)

Memory

-7.0MiB live, 82.4MiB allocated; 11ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 41 to 16 computations (61% saved)

preprocess27.0ms (1%)

Memory: 19.1MiB live, 68.0MiB allocated; 17ms collecting garbage
Remove: (abs x)
Compiler: Compiled 108 to 54 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample797.0ms (30.6%)

explain137.0ms (5.2%)

preprocess181.0ms (7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify112.0ms (4.3%)

localize32.0ms (1.2%)

series2.0ms (0.1%)

simplify140.0ms (5.4%)

rewrite50.0ms (1.9%)

eval15.0ms (0.6%)

prune2.0ms (0.1%)

simplify193.0ms (7.4%)

localize35.0ms (1.3%)

series1.0ms (0.1%)

simplify228.0ms (8.7%)

rewrite45.0ms (1.7%)

eval14.0ms (0.6%)

prune2.0ms (0.1%)

simplify123.0ms (4.7%)

localize21.0ms (0.8%)

series2.0ms (0.1%)

simplify205.0ms (7.9%)

rewrite46.0ms (1.8%)

eval5.0ms (0.2%)

prune3.0ms (0.1%)

regimes9.0ms (0.4%)

regimes5.0ms (0.2%)

regimes4.0ms (0.2%)

bsearch17.0ms (0.6%)

simplify81.0ms (3.1%)

derivations68.0ms (2.6%)

preprocess27.0ms (1%)

end0.0ms (0%)

Profiling