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

0.6MiB live, 0.6MiB 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)

sample1.3s (72.9%)

Memory

-63.6MiB live, 1 019.4MiB allocated; 1.1s collecting garbage

Samples

342.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-mult!: 90.0ms (77.2% of total)

ival-sub!: 25.0ms (21.5% of total)

adjust: 1.0ms (0.9% of total)

Bogosity

preprocess71.0ms (4%)

Memory

-13.6MiB live, 32.3MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	40	21
2	123	21
3	457	21
4	2752	21

Stop Event

1×	node-limit

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))

Symmetry

(abs x)

Compiler

Compiled 12 to 12 computations (0% saved)

series3.0ms (0.2%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Counts

6 → 6

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
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (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) x 2 1)
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)
1.0ms	x	@	0	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)

rewrite46.0ms (2.6%)

Memory

29.2MiB live, 75.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	82
0	25	80
1	113	80
0	678	75
1	2101	75

Stop Event

1×	saturated
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

12 → 86

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)
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

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

eval9.0ms (0.5%)

Memory: -17.8MiB live, 28.3MiB allocated; 2ms collecting garbage
Compiler: Compiled 378 to 179 computations (52.6% saved)

prune2.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	2	82

Accuracy

100.0%

Counts

82 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
▶	51.0%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 12 to 12 computations (0% saved)

series2.0ms (0.1%)

Memory

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

Counts

5 → 6

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx x #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

Calls

3 calls:

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

rewrite60.0ms (3.3%)

Memory

2.7MiB live, 58.5MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	86
0	26	78
1	139	29
0	1105	29
1	1569	29

Stop Event

1×	saturated
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

11 → 11

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 1.5MiB live, 1.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 29 to 21 computations (27.6% saved)

prune1.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	4	3	7
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	4	5	9

Accuracy

100.0%

Counts

9 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
▶	53.4%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
▶	32.0%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 1 binary64) x) x))
▶	2.7%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	51.0%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 36 to 36 computations (0% saved)

series5.0ms (0.3%)

Memory

-36.8MiB live, 9.9MiB allocated; 2ms collecting garbage

Counts

10 → 7

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* 1 x) x) #s(hole binary64 (pow x 2)))
#s(approx (* 1 x) #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (* (* x x) 2) 1) 2 (- (* (* x x) 2) 1) (* (* 1 x) x) (* 1 x) 1 x (+ (* x (+ x x)) -1) (+ x x) -1)
1.0ms	x	@	inf	((- (* (* x x) 2) 1) 2 (- (* (* x x) 2) 1) (* (* 1 x) x) (* 1 x) 1 x (+ (* x (+ x x)) -1) (+ x x) -1)
0.0ms	x	@	0	((- (* (* x x) 2) 1) 2 (- (* (* x x) 2) 1) (* (* 1 x) x) (* 1 x) 1 x (+ (* x (+ x x)) -1) (+ x x) -1)

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

rewrite73.0ms (4.1%)

Memory

24.6MiB live, 117.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	124
0	34	106
1	149	42
0	1300	42
1	1719	42

Stop Event

1×	saturated
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

17 → 31

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 5.7MiB live, 5.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 56 to 29 computations (48.2% saved)

prune2.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	12	6	18

Accuracy

100.0%

Counts

18 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
✓	53.4%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
✓	32.0%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 1 binary64) x) x))
▶	4.3%	#s(approx (- (* (* x x) 2) 1) x)
✓	2.7%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	51.0%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 43 to 43 computations (0% saved)

series1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Counts

2 → 5

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

Calls

3 calls:

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

rewrite49.0ms (2.7%)

Memory

-36.5MiB live, 60.2MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	69
0	19	67
1	102	67
0	667	61
1	2093	61

Stop Event

1×	saturated
1×	iter-limit
1×	node-limit
1×	saturated

Counts

7 → 7

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) x)
x
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

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

eval1.0ms (0%)

Memory: 1.1MiB live, 1.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 32 to 22 computations (31.3% saved)

prune2.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	0	0
Picked	0	1	1
Done	1	4	5
Total	4	6	10

Accuracy

100.0%

Counts

10 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
✓	53.4%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
	49.5%	#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
✓	4.3%	#s(approx (- (* (* x x) 2) 1) x)
✓	2.7%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	51.0%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 82 to 67 computations (18.3% saved)

regimes10.0ms (0.6%)

Memory

27.6MiB live, 27.6MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(*.f64 x x)
2.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`(*.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 13 to 13 computations (0% saved)

regimes9.0ms (0.5%)

Memory

-20.3MiB live, 25.8MiB allocated; 2ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
2.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 13 to 13 computations (0% saved)

regimes7.0ms (0.4%)

Memory

22.0MiB live, 22.0MiB allocated; 0ms 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) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) x)
(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
53.4%	1	`(*.f64 x x)`
53.4%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
53.4%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
53.4%	1	`x`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes7.0ms (0.4%)

Memory

-29.4MiB live, 17.5MiB allocated; 1ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(.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
53.8%	2	`(*.f64 x x)`
53.8%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
53.8%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
53.8%	2	`x`

Compiler

Compiled 13 to 13 computations (0% saved)

regimes5.0ms (0.3%)

Memory

17.1MiB live, 17.1MiB allocated; 0ms collecting garbage

Accuracy

Total -31.9b remaining (-101.7%)

Threshold costs -31.9b (-101.7%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 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
51.0%	1	`(*.f64 x x)`
51.0%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
51.0%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
51.0%	1	`x`

Compiler

Compiled 13 to 13 computations (0% saved)

bsearch12.0ms (0.7%)

Memory

-27.4MiB live, 22.8MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.06911277808823318	5338.632843186603

Samples

4.0ms

144×

valid

Compiler

Compiled 163 to 181 computations (-11% saved)

Precisions

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

ival-mult!: 1.0ms (62.6% of total)

ival-sub!: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

bsearch3.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.06911277808823318	5338.632843186603

Compiler

Compiled 145 to 163 computations (-12.4% saved)

derivations47.0ms (2.6%)

Memory

16.8MiB live, 60.5MiB allocated; 3ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 30 to 21 computations (30% saved)

preprocess54.0ms (3%)

Memory: 45.9MiB live, 122.0MiB allocated; 27ms collecting garbage
Remove: (abs x)
Compiler: Compiled 136 to 115 computations (15.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (72.9%)

preprocess71.0ms (4%)

series3.0ms (0.2%)

rewrite46.0ms (2.6%)

eval9.0ms (0.5%)

prune2.0ms (0.1%)

series2.0ms (0.1%)

rewrite60.0ms (3.3%)

eval1.0ms (0%)

prune1.0ms (0.1%)

series5.0ms (0.3%)

rewrite73.0ms (4.1%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

series1.0ms (0.1%)

rewrite49.0ms (2.7%)

eval1.0ms (0%)

prune2.0ms (0.1%)

regimes10.0ms (0.6%)

regimes9.0ms (0.5%)

regimes7.0ms (0.4%)

regimes7.0ms (0.4%)

regimes5.0ms (0.3%)

bsearch12.0ms (0.7%)

bsearch3.0ms (0.2%)

derivations47.0ms (2.6%)

preprocess54.0ms (3%)

end0.0ms (0%)

Profiling