Metrics for x / (x^2 + 1)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample660.0ms (63.3%)

Memory

-4.0MiB live, 713.5MiB allocated; 214ms collecting garbage

Samples

378.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-add!: 66.0ms (36.1% of total)

ival-div!: 64.0ms (35% of total)

ival-mult!: 51.0ms (27.9% of total)

adjust: 2.0ms (1.1% of total)

Bogosity

preprocess60.0ms (5.8%)

Memory

-13.2MiB live, 40.3MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	43	21
2	107	21
3	240	21
4	1527	21

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.3%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 14 to 10 computations (28.6% saved)

series6.0ms (0.6%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	259

Stop Event

1×	iter-limit

Counts

5 → 15

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (/ x (+ (* x x) 1)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))))))
#s(approx (/ x (+ (* x x) 1)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64))))))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(approx (+ (* x x) 1) (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) x))
#s(approx (+ (* x x) 1) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (/ x (+ (* x x) 1)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) x)))
#s(approx (/ x (+ (* x x) 1)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) x)))
#s(approx (/ x (+ (* x x) 1)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) x)))

Calls

3 calls:

Time	Variable	Point
1.0ms	x	inf
1.0ms	x	-inf
1.0ms	x	0

rewrite73.0ms (7%)

Memory

-13.8MiB live, 126.8MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	43	17
0	386	15

Stop Event

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

Counts

5 → 84

Calls

Call 1

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

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

eval19.0ms (1.8%)

Memory: 3.9MiB live, 48.6MiB allocated; 7ms collecting garbage
Compiler: Compiled 1 234 to 290 computations (76.5% saved)

prune2.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Accuracy

100.0%

Counts

96 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.3%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	54.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	48.1%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 26 to 18 computations (30.8% saved)

series4.0ms (0.4%)

Memory

13.9MiB live, 13.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	257

Stop Event

1×	iter-limit

Counts

7 → 15

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (/ x (+ (* x x) 1)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))))))
#s(approx (/ x (+ (* x x) 1)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64))))))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(approx (+ (* x x) 1) (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) x))
#s(approx (+ (* x x) 1) (pow.f64 x #s(literal 2 binary64)))
#s(approx (+ (* x x) 1) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (/ x (+ (* x x) 1)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) x)))
#s(approx (/ x (+ (* x x) 1)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) x)))
#s(approx (/ x (+ (* x x) 1)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) x)))

Calls

3 calls:

Time	Variable	Point
1.0ms	x	-inf
0.0ms	x	inf
0.0ms	x	0

rewrite60.0ms (5.8%)

Memory

7.6MiB live, 97.6MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	12	33
1	52	33
0	412	33

Stop Event

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

Counts

7 → 73

Calls

Call 1

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

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

eval7.0ms (0.7%)

Memory: 20.3MiB live, 20.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 134 to 249 computations (78% saved)

prune31.0ms (3%)

Memory

-33.3MiB live, 14.2MiB allocated; 17ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	80	3	83

Accuracy

100.0%

Counts

83 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	73.3%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	54.7%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	48.1%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes9.0ms (0.8%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

2 → 2

4 → 2

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) x)

Outputs
#s(approx (/ x (+ (* x x) 1)) x)

Call 2

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

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

Call 3

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
48.1%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
48.1%	1	`x`
85.5%	5	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.2%	2	`x`
99.9%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
100.0%	2	`x`

Compiler

Compiled 57 to 32 computations (43.9% saved)

bsearch2.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	29118.63927209447	453208670496357.25

Samples

0.0ms

16×

valid

Compiler

Compiled 27 to 23 computations (14.8% saved)

Precisions

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

adjust: 0.0ms (0% of total)

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

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

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

bsearch14.0ms (1.4%)

Memory

-12.8MiB live, 32.1MiB allocated; 6ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.3436298419443254e-9	8.195209715717231

Samples

8.0ms

160×

valid

Compiler

Compiled 210 to 169 computations (19.5% saved)

Precisions

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

ival-div!: 4.0ms (77.4% of total)

ival-mult!: 1.0ms (19.3% of total)

adjust: 0.0ms (0% of total)

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

derivations3.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 54 to 16 computations (70.4% saved)

preprocess93.0ms (8.9%)

Memory: -8.0MiB live, 218.3MiB allocated; 48ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 176 to 86 computations (51.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample660.0ms (63.3%)

preprocess60.0ms (5.8%)

series6.0ms (0.6%)

rewrite73.0ms (7%)

eval19.0ms (1.8%)

prune2.0ms (0.2%)

series4.0ms (0.4%)

rewrite60.0ms (5.8%)

eval7.0ms (0.7%)

prune31.0ms (3%)

regimes9.0ms (0.8%)

bsearch2.0ms (0.1%)

bsearch14.0ms (1.4%)

derivations3.0ms (0.3%)

preprocess93.0ms (8.9%)

end0.0ms (0%)

Profiling