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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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)

sample470.0ms (40.3%)

Memory

49.9MiB live, 569.5MiB allocated; 88ms collecting garbage

Samples

282.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-mult!: 99.0ms (78.8% of total)

ival-sub!: 25.0ms (19.9% of total)

adjust: 2.0ms (1.6% of total)

Bogosity

preprocess85.0ms (7.3%)

Memory

-45.4MiB live, 53.1MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	32	22
2	94	22
3	297	21
4	1672	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 14 to 12 computations (14.3% saved)

series3.0ms (0.2%)

Memory

5.3MiB live, 5.3MiB 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)

rewrite74.0ms (6.4%)

Memory

18.3MiB live, 111.0MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	82
0	25	80
1	96	80
0	529	75

Stop Event

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

Counts

12 → 87

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
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 x (+.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (log.f64 (.f64 x (+.f64 x x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64) #s(literal -1 binary64)) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (.f64 (log.f64 (.f64 x (+.f64 x x))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x 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) (neg.f64 x)) (neg.f64 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)) (-.f64 (*.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 (exp.f64 (log.f64 x)) (exp.f64 (log.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) (-.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) (-.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 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (fma.f64 x (+.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 x (+.f64 x x))) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))))
(-.f64 (*.f64 x (+.f64 x x)) #s(literal 1 binary64))
(+.f64 (*.f64 x (+.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))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(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 (exp.f64 (log.f64 x)) (exp.f64 (log.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 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.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 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
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))

eval7.0ms (0.6%)

Memory: 20.4MiB live, 20.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 931 to 209 computations (77.6% saved)

prune7.0ms (0.6%)

Memory

-37.9MiB live, 6.9MiB allocated; 7ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	2	83

Accuracy

100.0%

Counts

83 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
▶	48.4%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 15 to 12 computations (20% saved)

series2.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB 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))

rewrite99.0ms (8.5%)

Memory

22.5MiB live, 115.2MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	86
0	26	84
1	121	29
0	949	29

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
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 (0.1%)

Memory: 2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 56 to 21 computations (62.5% saved)

prune1.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB 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))
▶	51.1%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
▶	31.7%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 1 binary64) x) x))
▶	3.1%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	48.4%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 45 to 36 computations (20% saved)

series2.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms 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
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)
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

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)

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)

rewrite57.0ms (4.9%)

Memory

-19.8MiB live, 72.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	124
0	34	106
1	130	42
0	1035	42

Stop Event

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

Counts

17 → 36

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

eval2.0ms (0.2%)

Memory: 4.8MiB live, 4.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 409 to 52 computations (87.3% saved)

prune2.0ms (0.2%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	17	6	23

Accuracy

100.0%

Counts

23 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
✓	51.1%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
✓	31.7%	#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 1 binary64) x) x))
▶	4.7%	#s(approx (- (* (* x x) 2) 1) x)
✓	3.1%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	48.4%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 54 to 43 computations (20.4% saved)

series1.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB 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)

rewrite78.0ms (6.7%)

Memory

-0.7MiB live, 94.0MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	69
0	19	67
1	86	67
0	519	61

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
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: 1.3MiB live, 1.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 57 to 22 computations (61.4% saved)

prune2.0ms (0.2%)

Memory

6.0MiB live, 5.9MiB 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))
✓	51.1%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
	52.5%	#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
✓	4.7%	#s(approx (- (* (* x x) 2) 1) x)
✓	3.1%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	48.4%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 128 to 67 computations (47.7% saved)

regimes16.0ms (1.3%)

Memory

-17.3MiB live, 28.8MiB allocated; 8ms 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:

7.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
3.0ms	x
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 16 to 13 computations (18.8% saved)

regimes9.0ms (0.8%)

Memory

23.3MiB live, 23.3MiB allocated; 0ms 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:

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
99.1%	2	`(*.f64 x x)`
99.1%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
99.1%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
99.1%	2	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes12.0ms (1%)

Memory

-26.4MiB live, 19.4MiB 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) #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:

6.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	x
2.0ms	(*.f64 x x)
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
51.1%	1	`(*.f64 x x)`
51.1%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
51.1%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
51.1%	1	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.5%)

Memory

19.5MiB live, 19.5MiB allocated; 0ms 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:

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

Results

Accuracy	Segments	Branch
51.5%	2	`(*.f64 x x)`
51.5%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
51.5%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
51.5%	2	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.4%)

Memory

14.4MiB live, 14.4MiB 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) #s(literal 2 binary64))

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 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
50.3%	2	`x`
50.3%	2	`(*.f64 x x)`
50.3%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
50.3%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes10.0ms (0.9%)

Memory

-42.8MiB live, 13.1MiB allocated; 6ms 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:

7.0ms	(.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
48.4%	1	`(*.f64 x x)`
48.4%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
48.4%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
48.4%	1	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch10.0ms (0.8%)

Memory

16.7MiB live, 16.7MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.4816144486072554e-5	4.047920404007436

Samples

4.0ms

144×

valid

Compiler

Compiled 208 to 181 computations (13% saved)

Precisions

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

ival-mult!: 1.0ms (62.5% of total)

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

adjust: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999995609637	31.77131919435945

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch13.0ms (1.1%)

Memory

22.8MiB live, 22.8MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-0.9999999995609637	31.77131919435945

Samples

4.0ms

256×

valid

Compiler

Compiled 298 to 298 computations (0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0% of total)

derivations31.0ms (2.6%)

Memory

-18.5MiB live, 27.7MiB allocated; 8ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 105 to 31 computations (70.5% saved)

preprocess160.0ms (13.7%)

Memory: -7.0MiB live, 152.7MiB allocated; 116ms collecting garbage
Remove: (abs x)
Compiler: Compiled 322 to 169 computations (47.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample470.0ms (40.3%)

preprocess85.0ms (7.3%)

series3.0ms (0.2%)

rewrite74.0ms (6.4%)

eval7.0ms (0.6%)

prune7.0ms (0.6%)

series2.0ms (0.2%)

rewrite99.0ms (8.5%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

series2.0ms (0.2%)

rewrite57.0ms (4.9%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

series1.0ms (0.1%)

rewrite78.0ms (6.7%)

eval1.0ms (0%)

prune2.0ms (0.2%)

regimes16.0ms (1.3%)

regimes9.0ms (0.8%)

regimes12.0ms (1%)

regimes6.0ms (0.5%)

regimes5.0ms (0.4%)

regimes10.0ms (0.9%)

bsearch10.0ms (0.8%)

bsearch0.0ms (0%)

bsearch13.0ms (1.1%)

derivations31.0ms (2.6%)

preprocess160.0ms (13.7%)

end0.0ms (0%)

Profiling