x / (x^2 + 1)

Time bar (total: 2.4s)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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)

sample836.0ms (35.1%)

Memory
6.1MiB live, 1 215.3MiB allocated; 275ms collecting garbage
Samples
627.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 196.0ms
ival-add!: 89.0ms (45.4% of total)
ival-mult!: 67.0ms (34.2% of total)
ival-div!: 39.0ms (19.9% of total)
adjust: 2.0ms (1% of total)
Bogosity

preprocess53.0ms (2.2%)

Memory
4.0MiB live, 50.2MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01022
14321
211021
324521
4142721
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
73.3%
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Symmetry

(negabs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series3.0ms (0.1%)

Memory
11.6MiB live, 11.6MiB allocated; 0ms collecting garbage
Counts
5 → 15
Calls
Call 1
Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
Outputs
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))
Calls

3 calls:

TimeVariablePointExpression
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)

rewrite213.0ms (8.9%)

Memory
8.1MiB live, 306.9MiB allocated; 33ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066290
069252
1434246
24172242
08617220
132628220
Stop Event
saturated
node-limit
iter-limit
Counts
20 → 131
Calls
Call 1
Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ 1 x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))
Outputs
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) x)
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 x (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (neg.f64 x) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(neg.f64 (/.f64 (neg.f64 x) (fma.f64 x x #s(literal 1 binary64))))
x
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) x) x)
(*.f64 (+.f64 #s(literal 1 binary64) (fabs.f64 x)) (-.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)) (-.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (*.f64 x x))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 x (*.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(neg.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal -1 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) x) x #s(literal 1 binary64))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 x (neg.f64 x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (*.f64 x x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (*.f64 x x) #s(literal -1 binary64))
(-.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (neg.f64 (fabs.f64 (fabs.f64 x))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (fabs.f64 x))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (neg.f64 x))) #s(literal 2 binary64))
(pow.f64 (*.f64 (fabs.f64 (fabs.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (neg.f64 (fabs.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (neg.f64 (neg.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 (fabs.f64 x))) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fabs.f64 x))) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))
(pow.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal -1 binary64) x) #s(literal 2 binary64))
(pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (*.f64 (*.f64 (*.f64 x x) x) x))
(fabs.f64 (*.f64 x x))
(fabs.f64 (*.f64 (neg.f64 x) x))
#s(literal 1 binary64)
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) x) x #s(literal -1 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (*.f64 x x))) x))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (*.f64 x x))) x))

eval15.0ms (0.6%)

Memory
-5.2MiB live, 48.5MiB allocated; 4ms collecting garbage
Compiler

Compiled 641 to 354 computations (44.8% saved)

prune6.0ms (0.3%)

Memory
-30.5MiB live, 14.8MiB allocated; 4ms collecting garbage
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1203123
Fresh000
Picked101
Done000
Total1213124
Accuracy
100.0%
Counts
124 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
73.3%
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
54.7%
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
48.7%
#s(approx (/ x (+ (* x x) 1)) x)
Compiler

Compiled 18 to 18 computations (0% saved)

series2.0ms (0.1%)

Memory
10.2MiB live, 10.2MiB allocated; 0ms collecting garbage
Counts
7 → 15
Calls
Call 1
Inputs
#s(approx (/ x (+ (* x x) 1)) x)
x
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
Outputs
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((/ x (+ (* x x) 1)) x (/ x (+ (* x x) 1)) (/ 1 x) 1 (/ x (+ (* x x) 1)) (+ (* x x) 1))
1.0ms
x
@inf
((/ x (+ (* x x) 1)) x (/ x (+ (* x x) 1)) (/ 1 x) 1 (/ x (+ (* x x) 1)) (+ (* x x) 1))
0.0ms
x
@0
((/ x (+ (* x x) 1)) x (/ x (+ (* x x) 1)) (/ 1 x) 1 (/ x (+ (* x x) 1)) (+ (* x x) 1))

rewrite988.0ms (41.5%)

Memory
-49.1MiB live, 242.1MiB allocated; 1.0s collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067290
070250
1433244
24168240
08602236
132613236
Stop Event
saturated
node-limit
iter-limit
Counts
22 → 101
Calls
Call 1
Inputs
#s(approx (/ x (+ (* x x) 1)) x)
x
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 x))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- 1 (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))))
#s(approx (/ x (+ (* x x) 1)) #s(hole binary64 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))))
Outputs
#s(approx (/ x (+ (* x x) 1)) x)
x
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 x)))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)))
#s(literal 1 binary64)
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) x)
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 x (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (neg.f64 x) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))))
(neg.f64 (/.f64 (neg.f64 x) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) x) x)
(*.f64 (+.f64 #s(literal 1 binary64) (fabs.f64 x)) (-.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)) (-.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (*.f64 x x))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 x (*.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))))
(neg.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal -1 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) x) x #s(literal 1 binary64))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 (neg.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 x (neg.f64 x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 (*.f64 x x) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (*.f64 x x)))
(-.f64 (*.f64 x x) (*.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (*.f64 x x) #s(literal -1 binary64))
(-.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
#s(approx (/ x (+ (* x x) 1)) x)
#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) x) x #s(literal -1 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (*.f64 x x))) x))
#s(approx (+ (* x x) 1) (*.f64 x x))
#s(approx (+ (* x x) 1) (fma.f64 x x #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) x))
#s(approx (/ x (+ (* x x) 1)) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) #s(literal -1 binary64)) (*.f64 x x))) x))

eval8.0ms (0.4%)

Memory
28.7MiB live, 28.7MiB allocated; 0ms collecting garbage
Compiler

Compiled 438 to 241 computations (45% saved)

prune4.0ms (0.2%)

Memory
-39.0MiB live, 7.6MiB allocated; 2ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New89089
Fresh000
Picked033
Done000
Total89392
Accuracy
100.0%
Counts
92 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
73.3%
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
54.7%
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
48.7%
#s(approx (/ x (+ (* x x) 1)) x)
Compiler

Compiled 35 to 32 computations (8.6% saved)

regimes4.0ms (0.2%)

Memory
10.4MiB live, 10.4MiB 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))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Outputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
Calls

2 calls:

2.0ms
x
2.0ms
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
99.9%2(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
100.0%2x
Compiler

Compiled 6 to 6 computations (0% saved)

regimes3.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB 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

2 calls:

1.0ms
x
1.0ms
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
82.8%5(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
99.8%2x
Compiler

Compiled 6 to 6 computations (0% saved)

regimes2.0ms (0.1%)

Memory
7.8MiB live, 7.8MiB 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
AccuracySegmentsBranch
48.7%1(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
48.7%1x
Compiler

Compiled 6 to 6 computations (0% saved)

bsearch1.0ms (0.1%)

Memory
3.7MiB live, 3.7MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
predicate-same
Steps
TimeLeftRight
1.0ms
943531.6396695796
7905379877114.497
Samples
0.0ms16×0valid
Compiler

Compiled 22 to 23 computations (-4.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0% of total)
ival-add!: 0.0ms (0% of total)
ival-mult!: 0.0ms (0% of total)
ival-div!: 0.0ms (0% of total)

bsearch14.0ms (0.6%)

Memory
-21.8MiB live, 29.7MiB allocated; 4ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
13.0ms
4.486584672713174e-8
241709.32169964173
Samples
5.0ms160×0valid
Compiler

Compiled 150 to 169 computations (-12.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-mult!: 1.0ms (51.6% of total)
ival-div!: 1.0ms (51.6% of total)
adjust: 0.0ms (0% of total)
ival-add!: 0.0ms (0% of total)

derivations103.0ms (4.3%)

Memory
-11.4MiB live, 124.9MiB allocated; 7ms collecting garbage
Stop Event
done
Compiler

Compiled 20 to 16 computations (20% saved)

preprocess126.0ms (5.3%)

Memory
66.1MiB live, 236.6MiB allocated; 79ms collecting garbage
Remove

(negabs x)

Compiler

Compiled 99 to 86 computations (13.1% saved)

end0.0ms (0%)

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

Profiling

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