Metrics for x / (x^2 + 1)

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
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)

sample651.0ms (39.1%)

Memory

1.8MiB live, 976.5MiB allocated; 301ms collecting garbage

Samples

403.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 263.0ms

ival-div!: 168.0ms (63.8% of total)

ival-mult!: 75.0ms (28.5% of total)

ival-add!: 19.0ms (7.2% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

preprocess61.0ms (3.6%)

Memory

-18.6MiB live, 33.5MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	43	21
2	110	21
3	245	21
4	1427	21

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.6%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series3.0ms (0.2%)

Memory

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

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)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))

Calls

3 calls:

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

rewrite230.0ms (13.8%)

Memory

5.5MiB live, 205.9MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	290
0	69	252
1	434	246
2	4217	242
0	8528	220
1	34205	220

Stop Event

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

Counts

20 → 132

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)
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))

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

eval12.0ms (0.7%)

Memory: 23.1MiB live, 23.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 653 to 361 computations (44.7% saved)

prune7.0ms (0.4%)

Memory

-41.1MiB live, 7.6MiB allocated; 5ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	3	125

Accuracy

100.0%

Counts

125 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	50.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
▶	52.2%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 18 to 18 computations (0% saved)

series2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

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)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

((/ x (+ (* x x) 1)) x (/ x (+ (* x x) 1)) (/ 1 x) 1 (/ x (+ (* x x) 1)) (+ (* x x) 1))

0.0ms

inf

((/ x (+ (* x x) 1)) x (/ x (+ (* x x) 1)) (/ 1 x) 1 (/ x (+ (* x x) 1)) (+ (* x x) 1))

0.0ms

((/ x (+ (* x x) 1)) x (/ x (+ (* x x) 1)) (/ 1 x) 1 (/ x (+ (* x x) 1)) (+ (* x x) 1))

rewrite205.0ms (12.3%)

Memory

13.6MiB live, 201.7MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	290
0	70	250
1	433	244
2	4213	240
0	8573	236
1	34436	236

Stop Event

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

Counts

22 → 101

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))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))

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

eval8.0ms (0.5%)

Memory: 17.3MiB live, 17.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 438 to 241 computations (45% saved)

prune3.0ms (0.2%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	88	4	92

Accuracy

100.0%

Counts

92 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	27.1%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	50.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	52.2%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 25 to 25 computations (0% saved)

series2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Counts

4 → 15

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite255.0ms (15.3%)

Memory

29.1MiB live, 240.3MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	297
0	68	259
1	439	253
2	4253	249
0	8558	227
1	34318	227

Stop Event

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

Counts

19 → 74

Calls

Call 1

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

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

eval14.0ms (0.8%)

Memory: -38.2MiB live, 6.2MiB allocated; 7ms collecting garbage
Compiler: Compiled 400 to 230 computations (42.5% saved)

prune3.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	64	4	68

Accuracy

100.0%

Counts

68 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	27.1%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	50.6%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	52.2%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 47 to 41 computations (12.8% saved)

regimes4.0ms (0.2%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

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

2 calls:

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

Results

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

Compiler

Compiled 6 to 6 computations (0% saved)

regimes3.0ms (0.2%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
80.4%	4	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.0%	2	`x`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes2.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB 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 x) 1)) x)

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
52.2%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
52.2%	1	`x`

Compiler

Compiled 6 to 6 computations (0% saved)

bsearch1.0ms (0.1%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	61037207.998657666	1066352836.5899398

Samples

0.0ms

16×

valid

Compiler

Compiled 22 to 23 computations (-4.5% 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)

bsearch10.0ms (0.6%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.07720526249714202	223670.28238414953

Samples

4.0ms

144×

valid

Compiler

Compiled 136 to 153 computations (-12.5% saved)

Precisions

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

ival-mult!: 1.0ms (56.8% of total)

ival-div!: 1.0ms (56.8% of total)

adjust: 0.0ms (0% of total)

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

derivations89.0ms (5.3%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess103.0ms (6.2%)

Memory: -23.1MiB live, 41.2MiB allocated; 37ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 99 to 86 computations (13.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample651.0ms (39.1%)

preprocess61.0ms (3.6%)

series3.0ms (0.2%)

rewrite230.0ms (13.8%)

eval12.0ms (0.7%)

prune7.0ms (0.4%)

series2.0ms (0.1%)

rewrite205.0ms (12.3%)

eval8.0ms (0.5%)

prune3.0ms (0.2%)

series2.0ms (0.1%)

rewrite255.0ms (15.3%)

eval14.0ms (0.8%)

prune3.0ms (0.2%)

regimes4.0ms (0.2%)

regimes3.0ms (0.2%)

regimes2.0ms (0.1%)

bsearch1.0ms (0.1%)

bsearch10.0ms (0.6%)

derivations89.0ms (5.3%)

preprocess103.0ms (6.2%)

end0.0ms (0%)

Profiling