Metrics for x / (x^2 + 1)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample498.0ms (38.3%)

Memory

5.2MiB live, 906.3MiB allocated; 102ms collecting garbage

Samples

284.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-mult!: 51.0ms (43.4% of total)

ival-div!: 41.0ms (34.9% of total)

ival-add!: 24.0ms (20.4% of total)

adjust: 2.0ms (1.7% of total)

Bogosity

explain61.0ms (4.7%)

Memory

-1.1MiB live, 144.9MiB allocated; 11ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
70	-	-	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	n/o	70	0
↳	`(*.f64 x x)`	overflow	70
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	70

Confusion

	Predicted +	Predicted -
+	70	0
-	0	186

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	70	0	0
-	0	0	186

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	186
1	70

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

20.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult!: 4.0ms (50.4% of total)

ival-div!: 2.0ms (25.2% of total)

ival-add!: 1.0ms (12.6% of total)

adjust: 0.0ms (0% of total)

preprocess78.0ms (6%)

Memory

-38.9MiB live, 63.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	28	22
2	62	21
3	91	21
4	164	21
5	408	21
6	2768	21
7	6481	21

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.5%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 14 to 10 computations (28.6% saved)

series3.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Counts

5 → 17

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 #s(hole binary64 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) #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)))
#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)

rewrite120.0ms (9.2%)

Memory

15.8MiB live, 156.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	302
0	72	267
1	361	257
0	3689	234

Stop Event

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

Counts

22 → 111

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 #s(hole binary64 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) #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)))
#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 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(/.f64 (neg.f64 x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (/.f64 (neg.f64 x) (fma.f64 x x #s(literal 1 binary64))))
(neg.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
x
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (.f64 x x))
(.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)))
(*.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 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1 binary64)) (.f64 x x)) (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (.f64 (.f64 x x) (+.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(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) (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 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)) #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 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.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 (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 (*.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 x x #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(-.f64 (.f64 x x) (.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))) (*.f64 x x)))
(-.f64 (.f64 x x) (.f64 (*.f64 (neg.f64 x) x) (pow.f64 x #s(literal -2 binary64))))
(-.f64 (*.f64 x x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x))))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 x 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 #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 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 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))
(fabs.f64 (*.f64 x x))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(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))))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) x))
#s(approx x 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)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -6 binary64))) 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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -4 binary64))) (neg.f64 x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 x #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64))) (neg.f64 x)))

eval19.0ms (1.4%)

Memory: -5.5MiB live, 44.3MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 346 to 340 computations (74.7% saved)

prune4.0ms (0.3%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Accuracy

100.0%

Counts

109 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	32.4%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
▶	58.0%	#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
▶	57.1%	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x))
▶	44.3%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 104 to 72 computations (30.8% saved)

series4.0ms (0.3%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Counts

16 → 28

Calls

Call 1

Inputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
x
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) x)
(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
#s(approx (+ (* x x) 1) (*.f64 x x))
(*.f64 x x)
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x)
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(pow.f64 x #s(literal -2 binary64))
#s(literal -2 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 #s(hole binary64 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) #s(hole binary64 (pow x 2)))
#s(approx (pow x -1) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ -1 (pow x 3))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 3))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ -1 (pow x 2))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 2))))
#s(approx (pow x -2) #s(hole binary64 (/ 1 (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)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (- 1 (pow x -2)) #s(hole binary64 1))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (- 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))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

rewrite133.0ms (10.2%)

Memory

-33.2MiB live, 205.0MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	494
0	108	454
1	432	430
0	4119	426

Stop Event

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

Counts

44 → 258

Calls

Call 1

Inputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
x
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) x)
(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
#s(approx (+ (* x x) 1) (*.f64 x x))
(*.f64 x x)
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x)
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(pow.f64 x #s(literal -2 binary64))
#s(literal -2 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 #s(hole binary64 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) #s(hole binary64 (pow x 2)))
#s(approx (pow x -1) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ -1 (pow x 3))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 3))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ -1 (pow x 2))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 2))))
#s(approx (pow x -2) #s(hole binary64 (/ 1 (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)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (- 1 (pow x -2)) #s(hole binary64 1))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (- 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))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))

Outputs
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(/.f64 (neg.f64 x) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (/.f64 (neg.f64 x) (fma.f64 x x #s(literal 1 binary64))))
(neg.f64 (/.f64 x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
x
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (.f64 x x))
(.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)))
(*.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 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1 binary64)) (.f64 x x)) (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (.f64 (.f64 x x) (+.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #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 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)) #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) (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 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.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 (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 (*.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 x x #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (.f64 x x) (.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))) (*.f64 x x)))
(-.f64 (.f64 x x) (.f64 (*.f64 (neg.f64 x) x) (pow.f64 x #s(literal -2 binary64))))
(-.f64 (*.f64 x x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x))))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) 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 (neg.f64 x) #s(approx (+ (* x x) 1) (*.f64 x x))))
(neg.f64 (/.f64 x (neg.f64 #s(approx (+ (* x x) 1) (*.f64 x x)))))
#s(approx (+ (* x x) 1) (*.f64 x x))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(.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 #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 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 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))
(fabs.f64 (*.f64 x x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(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))))
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 (neg.f64 x) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (/.f64 (neg.f64 x) (.f64 x x)) (/.f64 (neg.f64 x) x))
(*.f64 (/.f64 (fabs.f64 x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 (fabs.f64 x) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (/.f64 (fabs.f64 x) (.f64 x x)) (/.f64 (fabs.f64 x) x))
(*.f64 (/.f64 x (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (/.f64 x (.f64 x x)) (/.f64 x x))
(.f64 (/.f64 (neg.f64 x) x) (/.f64 (neg.f64 x) (.f64 x x)))
(.f64 (/.f64 (fabs.f64 x) x) (/.f64 (fabs.f64 x) (.f64 x x)))
(.f64 (/.f64 x x) (/.f64 x (.f64 x x)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (neg.f64 (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (neg.f64 x) (/.f64 (neg.f64 x) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (fabs.f64 x) (/.f64 (fabs.f64 x) (pow.f64 x #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(*.f64 x (/.f64 x (pow.f64 x #s(literal 3 binary64))))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 (/.f64 (*.f64 x x) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 (.f64 x x) x) (.f64 x x))
(/.f64 (*.f64 (neg.f64 x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(/.f64 (*.f64 x x) (pow.f64 x #s(literal 3 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 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) x))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(exp.f64 (-.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) (.f64 (log.f64 x) #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal -1 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal -1 binary64))))
#s(literal -1 binary64)
#s(approx (/ x (+ (* x x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) x) (*.f64 x x))
(/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 x #s(literal -4 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))) (neg.f64 (neg.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) x) (.f64 (neg.f64 x) (pow.f64 x #s(literal -2 binary64)))) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 x (.f64 x (pow.f64 x #s(literal -2 binary64)))) (.f64 x x))
(/.f64 (-.f64 (.f64 (.f64 x x) (pow.f64 x #s(literal 3 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 6 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 x #s(literal -6 binary64))) (+.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -6 binary64))) (*.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))) (neg.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x)
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 x #s(literal 3 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))) x))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) (neg.f64 x)))
(-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (+.f64 (pow.f64 x #s(literal -6 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 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))))
(*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (.f64 x x))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -6 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64)))) (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(/.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 (-.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (*.f64 (neg.f64 x) x)) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -6 binary64))) (+.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (neg.f64 x) x))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (neg.f64 x) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal -6 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal -4 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (pow.f64 x #s(literal -1 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 x)) (/.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal -1 binary64)) (pow.f64 (fabs.f64 x) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -2 binary64))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) x)
(/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 #s(literal -2 binary64) (.f64 (.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal -2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1 binary64) (*.f64 (log.f64 x) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1 binary64)))
(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))))
#s(literal -2 binary64)
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) x))
#s(approx x 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 (pow x -1) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (- 1 (pow x -2)) x) (neg.f64 (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ (- 1 (pow x -2)) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (- 1 (pow x -2)) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
#s(approx (- 1 (pow x -2)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
#s(approx (pow x -2) (pow.f64 x #s(literal -2 binary64)))
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (-.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) x) (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -6 binary64))) x))
#s(approx (+ (* x x) 1) (*.f64 x x))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (/ (- 1 (pow x -2)) x) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (- 1 (pow x -2)) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (- 1 (pow x -2)) #s(literal 1 binary64))
#s(approx (- 1 (pow x -2)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -4 binary64))) (neg.f64 x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 x #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64))) (neg.f64 x)))
#s(approx (/ (- 1 (pow x -2)) x) (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 x)))

eval23.0ms (1.8%)

Memory: 20.3MiB live, 67.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 4 103 to 849 computations (79.3% saved)

prune6.0ms (0.4%)

Memory

16.8MiB live, 16.8MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	245	5	250

Accuracy

100.0%

Counts

250 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	32.4%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
▶	57.1%	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
▶	58.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))
✓	44.3%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 60 to 40 computations (33.3% saved)

series4.0ms (0.3%)

Memory

-35.8MiB live, 11.4MiB allocated; 1ms collecting garbage

Counts

10 → 32

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))
(/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x)
#s(approx (- 1 (pow x -2)) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.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 (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ -1 (pow x 3))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 3))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ -1 (pow x 2))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 2))))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ -1 (pow x 3))))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 3))))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 (/ -1 (pow x 2))))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 2))))
#s(approx (/ 1 (* x x)) #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 (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (- 1 (pow x -2)) #s(hole binary64 1))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (- 1 (/ 1 (pow x 2)))))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 1))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 (- 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))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((/ x (+ (* x x) 1)) (/ (- 1 (pow x -2)) x) (- 1 (pow x -2)) 1 x (/ x (+ (* x x) 1)) (/ (- 1 (/ 1 (* x x))) x) (- 1 (/ 1 (* x x))) (/ 1 (* x x)) (* x x))
1.0ms	x	@	inf	((/ x (+ (* x x) 1)) (/ (- 1 (pow x -2)) x) (- 1 (pow x -2)) 1 x (/ x (+ (* x x) 1)) (/ (- 1 (/ 1 (* x x))) x) (- 1 (/ 1 (* x x))) (/ 1 (* x x)) (* x x))
1.0ms	x	@	-inf	((/ x (+ (* x x) 1)) (/ (- 1 (pow x -2)) x) (- 1 (pow x -2)) 1 x (/ x (+ (* x x) 1)) (/ (- 1 (/ 1 (* x x))) x) (- 1 (/ 1 (* x x))) (/ 1 (* x x)) (* x x))

Time

Variable

Point

Expression

2.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

rewrite135.0ms (10.4%)

Memory

33.9MiB live, 210.4MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	592
0	104	531
1	427	493
0	3928	476

Stop Event

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

Counts

42 → 163

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))
(/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x)
#s(approx (- 1 (pow x -2)) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.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 (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ -1 (pow x 3))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 3))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ -1 (pow x 2))))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 2))))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ -1 (pow x 3))))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 3))))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 (/ -1 (pow x 2))))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 (/ (- (pow x 2) 1) (pow x 2))))
#s(approx (/ 1 (* x x)) #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 (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (- 1 (pow x -2)) #s(hole binary64 1))
#s(approx (- 1 (pow x -2)) #s(hole binary64 (- 1 (/ 1 (pow x 2)))))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 1))
#s(approx (- 1 (/ 1 (* x x))) #s(hole binary64 (- 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))))
#s(approx (/ (- 1 (pow x -2)) x) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ (- 1 (/ 1 (* x x))) x) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))

Outputs
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))
(/.f64 (neg.f64 (neg.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x)
(neg.f64 (/.f64 (neg.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64))) x))
(neg.f64 (/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) (neg.f64 x)))
#s(approx (- 1 (pow x -2)) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (/ x (+ (* x x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) x) (*.f64 x x))
(/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 x #s(literal -4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) x) (.f64 (neg.f64 x) (pow.f64 x #s(literal -2 binary64)))) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 x (.f64 x (pow.f64 x #s(literal -2 binary64)))) (.f64 x x))
(/.f64 (-.f64 (.f64 (.f64 x x) (pow.f64 x #s(literal 3 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 x #s(literal 6 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 x #s(literal -6 binary64))) (+.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -6 binary64))) (*.f64 (+.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -4 binary64))) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))) (neg.f64 x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) x)
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))) x))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 x #s(literal 3 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) (neg.f64 x)))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (.f64 x x))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64)))) (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -6 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -4 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (.f64 x x) (pow.f64 x #s(literal -1 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (*.f64 (neg.f64 x) x)) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1 binary64)))) (*.f64 #s(literal 2 binary64) x))
(/.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(/.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -4 binary64))) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -6 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -4 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (neg.f64 x) x))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (neg.f64 x) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal -4 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -4 binary64)))) (/.f64 (pow.f64 x #s(literal -6 binary64)) (+.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -4 binary64)))))
(-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (pow.f64 x #s(literal -1 binary64))))
(.f64 (pow.f64 (.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 x)) (/.f64 #s(literal 1 binary64) (fabs.f64 x)))
(.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal -1 binary64)) (pow.f64 (fabs.f64 x) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -2 binary64))) #s(literal 2 binary64))
(/.f64 (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1 binary64))) (.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) x)
(/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal -2 binary64) (.f64 (.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (neg.f64 (pow.f64 x #s(literal -2 binary64))))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal -2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1 binary64)))
(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))))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(.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 #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 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 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))
(fabs.f64 (*.f64 x x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(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))))
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) x))
#s(approx (/ (- 1 (pow x -2)) x) (neg.f64 (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ (- 1 (pow x -2)) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (- 1 (pow x -2)) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
#s(approx (- 1 (pow x -2)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
#s(approx x x)
#s(approx (/ (- 1 (pow x -2)) x) (neg.f64 (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ (- 1 (pow x -2)) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (- 1 (pow x -2)) (neg.f64 (pow.f64 x #s(literal -2 binary64))))
#s(approx (- 1 (pow x -2)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
#s(approx (/ 1 (* x x)) (pow.f64 x #s(literal -2 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (-.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) x) (pow.f64 x #s(literal -3 binary64))))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -6 binary64))) x))
#s(approx (/ (- 1 (pow x -2)) x) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (- 1 (pow x -2)) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (- 1 (pow x -2)) #s(literal 1 binary64))
#s(approx (- 1 (pow x -2)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
#s(approx (/ (- 1 (pow x -2)) x) (pow.f64 x #s(literal -1 binary64)))
#s(approx (/ (- 1 (pow x -2)) x) (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -3 binary64))))
#s(approx (- 1 (pow x -2)) #s(literal 1 binary64))
#s(approx (- 1 (pow x -2)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -4 binary64))) (neg.f64 x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) (pow.f64 x #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal -1 binary64))) (neg.f64 x)))
#s(approx (/ (- 1 (pow x -2)) x) (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 x)))
#s(approx (/ (- 1 (pow x -2)) x) (/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 x)))

eval38.0ms (2.9%)

Memory: -11.0MiB live, 43.3MiB allocated; 24ms collecting garbage
Compiler: Compiled 2 929 to 653 computations (77.7% saved)

prune4.0ms (0.3%)

Memory

12.7MiB live, 12.7MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	145	5	150

Accuracy

100.0%

Counts

150 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	32.4%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	57.1%	#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x))
✓	58.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))
✓	44.3%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 153 to 72 computations (52.9% saved)

regimes9.0ms (0.7%)

Memory

-36.1MiB live, 13.5MiB allocated; 4ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	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 8 to 6 computations (25% saved)

regimes2.0ms (0.2%)

Memory

6.6MiB live, 6.7MiB 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(approx (- 1 (pow x -2)) #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(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB 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(approx (- 1 (pow x -2)) #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(approx (- 1 (pow x -2)) #s(literal 1 binary64)) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
79.8%	3	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
98.4%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0.2%)

Memory

6.8MiB live, 6.8MiB 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
44.3%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
44.3%	1	`x`

Compiler

Compiled 8 to 6 computations (25% 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	1314.3317874940992	34579626.86985456

Samples

1.0ms

16×

valid

Compiler

Compiled 33 to 26 computations (21.2% 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)

bsearch1.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	34579626.86985456	588867731.1756146

Samples

0.0ms

16×

valid

Compiler

Compiled 33 to 27 computations (18.2% 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)

bsearch7.0ms (0.5%)

Memory

15.4MiB live, 15.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	0.5173310153370478	5.464965006839764

Samples

3.0ms

96×

valid

Compiler

Compiled 166 to 129 computations (22.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult!: 1.0ms (83.5% of total)

adjust: 0.0ms (0% of total)

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

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

derivations67.0ms (5.1%)

Memory

-19.8MiB live, 75.1MiB allocated; 4ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 93 to 28 computations (69.9% saved)

preprocess78.0ms (6%)

Memory: 9.8MiB live, 152.0MiB allocated; 12ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 400 to 184 computations (54% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample498.0ms (38.3%)

explain61.0ms (4.7%)

preprocess78.0ms (6%)

series3.0ms (0.2%)

rewrite120.0ms (9.2%)

eval19.0ms (1.4%)

prune4.0ms (0.3%)

series4.0ms (0.3%)

rewrite133.0ms (10.2%)

eval23.0ms (1.8%)

prune6.0ms (0.4%)

series4.0ms (0.3%)

rewrite135.0ms (10.4%)

eval38.0ms (2.9%)

prune4.0ms (0.3%)

regimes9.0ms (0.7%)

regimes2.0ms (0.2%)

regimes3.0ms (0.2%)

regimes2.0ms (0.2%)

bsearch2.0ms (0.1%)

bsearch1.0ms (0.1%)

bsearch7.0ms (0.5%)

derivations67.0ms (5.1%)

preprocess78.0ms (6%)

end0.0ms (0%)

Profiling