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)

sample641.0ms (37%)

Memory

8.1MiB live, 540.2MiB allocated; 125ms collecting garbage

Samples

401.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 192.0ms

ival-mult!: 84.0ms (43.8% of total)

ival-add!: 64.0ms (33.4% of total)

ival-div!: 42.0ms (21.9% of total)

adjust: 2.0ms (1% of total)

Bogosity

explain78.0ms (4.5%)

Memory

10.0MiB live, 56.5MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
74	-	-	`(/.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	74	0
↳	`(*.f64 x x)`	overflow	74
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	74

Confusion

	Predicted +	Predicted -
+	74	0
-	0	182

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	74	0	0
-	0	0	182

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	182
1	74

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult!: 3.0ms (44.4% of total)

ival-div!: 2.0ms (29.6% of total)

ival-add!: 1.0ms (14.8% of total)

adjust: 0.0ms (0% of total)

preprocess231.0ms (13.3%)

Memory

-0.5MiB live, 228.2MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (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
0	5	7
0	8	7
1	15	7
2	37	7
3	77	7
4	138	7
5	347	7
6	2391	7
7	5991	7
0	8230	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.1%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

series3.0ms (0.2%)

Memory

5.9MiB live, 5.9MiB 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)

rewrite148.0ms (8.5%)

Memory

-25.5MiB live, 118.6MiB allocated; 19ms 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)))

eval11.0ms (0.6%)

Memory: 27.0MiB live, 27.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 388 to 341 computations (75.4% saved)

prune5.0ms (0.3%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Accuracy

100.0%

Counts

115 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.1%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	32.0%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
▶	59.0%	#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
▶	42.8%	#s(approx (/ x (+ (* x x) 1)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
▶	43.8%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 100 to 68 computations (32% saved)

series7.0ms (0.4%)

Memory

-34.3MiB live, 9.3MiB allocated; 4ms collecting garbage

Counts

15 → 24

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

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	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)) (- x (pow x 3)) (pow x 3) 3)
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)) (- x (pow x 3)) (pow x 3) 3)
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)) (- x (pow x 3)) (pow x 3) 3)

Time

Variable

Point

Expression

5.0ms

-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)) (- x (pow x 3)) (pow x 3) 3)

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)) (- x (pow x 3)) (pow x 3) 3)

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)) (- x (pow x 3)) (pow x 3) 3)

rewrite132.0ms (7.6%)

Memory

18.9MiB live, 172.9MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	429
0	98	382
1	418	372
0	3976	368

Stop Event

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

Counts

39 → 190

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

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 4 binary64)) #s(literal 1 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 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 -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 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (-.f64 #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 (-.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 (.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 (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 (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 (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))
#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 (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 #s(literal 1 binary64) (pow.f64 x #s(literal -1 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 #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) x))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(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 x (pow.f64 x #s(literal 3 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) x) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64) #s(literal 1 binary64)) x) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (neg.f64 x) x)))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (neg.f64 x) x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 3 binary64))) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 (neg.f64 (fma.f64 x x (neg.f64 (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)))) (neg.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 (fma.f64 x x (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64))) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(fma.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (.f64 x #s(literal -1 binary64)) (.f64 x x) x)
(fma.f64 (.f64 #s(literal -1 binary64) x) (.f64 x x) x)
(fma.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) x)
(fma.f64 (neg.f64 x) (*.f64 x x) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) x)
(fma.f64 (*.f64 (neg.f64 x) x) x x)
(fma.f64 (.f64 x x) (.f64 x #s(literal -1 binary64)) x)
(fma.f64 (.f64 x x) (.f64 #s(literal -1 binary64) x) x)
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 x (*.f64 (neg.f64 x) x) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 (pow.f64 x #s(literal 9 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(+.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) x)
(+.f64 x (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(.f64 (.f64 x (fabs.f64 x)) (fabs.f64 x))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) x))
(.f64 (.f64 (neg.f64 x) x) (neg.f64 x))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))))
#s(literal 3 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 (- x (pow x 3)) x)
#s(approx (- x (pow x 3)) (-.f64 x (pow.f64 x #s(literal 3 binary64))))
#s(approx (pow x 3) (pow.f64 x #s(literal 3 binary64)))
#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 (pow x 3)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
#s(approx (- x (pow x 3)) (*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 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 (- x (pow x 3)) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))))

eval38.0ms (2.2%)

Memory: -1.1MiB live, 45.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 2 940 to 562 computations (80.9% saved)

prune7.0ms (0.4%)

Memory

13.8MiB live, 13.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	204	4	208

Accuracy

100.0%

Counts

208 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	73.1%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	42.8%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
▶	59.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	43.8%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 41 to 27 computations (34.1% saved)

series37.0ms (2.1%)

Memory

-41.1MiB live, 5.8MiB allocated; 2ms collecting garbage

Counts

8 → 20

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
35.0ms	x	@	-inf	((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* (* (neg x) x) x) x) (* (neg x) x) (neg x))
1.0ms	x	@	inf	((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* (* (neg x) x) x) x) (* (neg x) x) (neg x))
1.0ms	x	@	0	((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* (* (neg x) x) x) x) (* (neg x) x) (neg x))

Time

Variable

Point

Expression

35.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite111.0ms (6.4%)

Memory

10.1MiB live, 150.2MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	380
0	87	340
1	391	315
0	3744	298

Stop Event

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

Counts

28 → 80

Calls

Call 1

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

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

eval8.0ms (0.5%)

Memory: 24.6MiB live, 24.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 513 to 266 computations (82.4% saved)

prune5.0ms (0.3%)

Memory

12.8MiB live, 12.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	86	4	90

Accuracy

100.0%

Counts

90 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	73.1%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	42.8%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
✓	59.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
✓	43.8%	#s(approx (/ x (+ (* x x) 1)) x)

Compiler

Compiled 124 to 54 computations (56.5% saved)

regimes6.0ms (0.4%)

Memory

-34.1MiB live, 13.0MiB allocated; 2ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

4.0ms	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)

regimes4.0ms (0.2%)

Memory

9.0MiB live, 9.0MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) (fma.f64 (*.f64 (neg.f64 x) x) x x))
#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
85.7%	6	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.4%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes1.0ms (0.1%)

Memory

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

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB 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
43.8%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
43.8%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch3.0ms (0.2%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
2.0ms	101282.15576672283	99951923578.96419

Samples

1.0ms

32×

valid

Compiler

Compiled 44 to 37 computations (15.9% 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)

bsearch11.0ms (0.6%)

Memory

16.3MiB live, 16.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.24646986050229766	101282.15576672283

Samples

4.0ms

144×

valid

Compiler

Compiled 244 to 180 computations (26.2% saved)

Precisions

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

ival-mult!: 1.0ms (56.9% of total)

ival-div!: 1.0ms (56.9% of total)

adjust: 0.0ms (0% of total)

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

bsearch7.0ms (0.4%)

Memory

-49.5MiB live, 8.9MiB allocated; 4ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	0.24646986050229766	101282.15576672283

Samples

1.0ms

32×

valid

Compiler

Compiled 190 to 153 computations (19.5% 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)

simplify49.0ms (2.8%)

Memory

35.7MiB live, 35.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	84
1	34	84
2	61	84
3	103	84
4	155	84
5	362	84
6	2695	84
7	6795	84

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 200000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (neg.f64 x) x) x x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) x) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) x)

Outputs
(if (<=.f64 x #s(literal 200000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (neg.f64 x) x) x x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ x (+ (* x x) 1)) x) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) x)

derivations91.0ms (5.2%)

Memory

-25.3MiB live, 20.9MiB allocated; 5ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 84 to 23 computations (72.6% saved)

preprocess99.0ms (5.7%)

Memory: -4.1MiB live, 40.2MiB allocated; 7ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 364 to 156 computations (57.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample641.0ms (37%)

explain78.0ms (4.5%)

preprocess231.0ms (13.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series3.0ms (0.2%)

rewrite148.0ms (8.5%)

eval11.0ms (0.6%)

prune5.0ms (0.3%)

series7.0ms (0.4%)

rewrite132.0ms (7.6%)

eval38.0ms (2.2%)

prune7.0ms (0.4%)

series37.0ms (2.1%)

rewrite111.0ms (6.4%)

eval8.0ms (0.5%)

prune5.0ms (0.3%)

regimes6.0ms (0.4%)

regimes4.0ms (0.2%)

regimes1.0ms (0.1%)

regimes2.0ms (0.1%)

bsearch3.0ms (0.2%)

bsearch11.0ms (0.6%)

bsearch7.0ms (0.4%)

simplify49.0ms (2.8%)

derivations91.0ms (5.2%)

preprocess99.0ms (5.7%)

end0.0ms (0%)

Profiling