Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

Time bar (total: 1.0s)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample442.0ms (43.3%)

Memory
-33.4MiB live, 776.4MiB allocated; 96ms collecting garbage
Samples
267.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 115.0ms
ival-mult!: 93.0ms (81% of total)
ival-sub!: 20.0ms (17.4% of total)
adjust: 2.0ms (1.7% of total)
Bogosity

explain55.0ms (5.4%)

Memory
13.0MiB live, 112.2MiB allocated; 4ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
00-0-#s(literal 2 binary64)
00-0-#s(literal 1 binary64)
00-0-(*.f64 (*.f64 x x) #s(literal 2 binary64))
00-0-(*.f64 x x)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
18.0ms512×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-mult!: 5.0ms (81.1% of total)
ival-sub!: 1.0ms (16.2% of total)
adjust: 0.0ms (0% of total)

preprocess49.0ms (4.8%)

Memory
-14.3MiB live, 32.6MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01122
12922
28322
323722
475721
5387821
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Symmetry

(abs x)

Compiler

Compiled 14 to 12 computations (14.3% saved)

series3.0ms (0.3%)

Memory
6.7MiB live, 6.7MiB allocated; 0ms collecting garbage
Counts
6 → 7
Calls
Call 1
Inputs
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)
Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)
1.0ms
x
@-inf
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)
1.0ms
x
@0
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)

rewrite74.0ms (7.2%)

Memory
14.4MiB live, 108.4MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02395
02693
19793
053887
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
13 → 88
Calls
Call 1
Inputs
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Outputs
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 x (+.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log.f64 (*.f64 x (+.f64 x x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64) #s(literal -1 binary64)) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (*.f64 (log.f64 (*.f64 x (+.f64 x x))) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64))))
(fma.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal -1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (+.f64 (fabs.f64 x) (fabs.f64 x)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 x (+.f64 x x)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x x)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 x (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
(fma.f64 x (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(fma.f64 x x (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64)) (fma.f64 x (+.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64)) (*.f64 x (+.f64 x x))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 4 binary64) (fma.f64 x (+.f64 x x) #s(literal 1 binary64)))))
(-.f64 (*.f64 x (+.f64 x x)) #s(literal 1 binary64))
(+.f64 (*.f64 x x) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x (+.f64 x x)) #s(literal -1 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)))
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (+.f64 (fabs.f64 x) (fabs.f64 x)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 (*.f64 x (+.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x x)))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 x (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 (*.f64 x (+.f64 x x)) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 x x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) (pow.f64 (*.f64 x x) #s(literal 3 binary64))) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (*.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x (*.f64 x x))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x x) (*.f64 x 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) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 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))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(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))))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (fma.f64 x (+.f64 x x) #s(literal -1 binary64)))
#s(approx (* (* x x) 2) (*.f64 x (+.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x))

eval8.0ms (0.7%)

Memory
20.7MiB live, 20.7MiB allocated; 0ms collecting garbage
Compiler

Compiled 944 to 213 computations (77.4% saved)

prune3.0ms (0.3%)

Memory
6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New80383
Fresh000
Picked101
Done000
Total81384
Accuracy
100.0%
Counts
84 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
52.1%
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
49.2%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Compiler

Compiled 28 to 21 computations (25% saved)

series10.0ms (1%)

Memory
-35.1MiB live, 14.1MiB allocated; 6ms collecting garbage
Counts
7 → 11
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx x #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Calls

3 calls:

TimeVariablePointExpression
6.0ms
x
@0
((- (* (* x x) 2) 1) -1 (- (* (* x x) 2) 1) (* x (+ x x)) x (+ x x) (+ (* x (+ x x)) -1))
1.0ms
x
@-inf
((- (* (* x x) 2) 1) -1 (- (* (* x x) 2) 1) (* x (+ x x)) x (+ x x) (+ (* x (+ x x)) -1))
1.0ms
x
@inf
((- (* (* x x) 2) 1) -1 (- (* (* x x) 2) 1) (* x (+ x x)) x (+ x x) (+ (* x (+ x x)) -1))

rewrite83.0ms (8.1%)

Memory
6.9MiB live, 101.5MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032167
036169
113352
098252
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
18 → 18
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx x #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Outputs
#s(approx (+ (* x (+ x x)) -1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (+ (* x (+ x x)) -1) #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(approx (+ (* x (+ x x)) -1) #s(literal -1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(approx x x)
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal -1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 2 binary64))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* x (+ x x)) -1) #s(literal 2 binary64))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))

eval1.0ms (0.1%)

Memory
2.9MiB live, 2.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 134 to 35 computations (73.9% saved)

prune2.0ms (0.2%)

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

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New10313
Fresh000
Picked033
Done000
Total10616
Accuracy
100.0%
Counts
16 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
52.1%
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
2.9%
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
49.2%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
28.7%
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
2.9%
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
Compiler

Compiled 65 to 48 computations (26.2% saved)

series2.0ms (0.2%)

Memory
5.2MiB live, 5.2MiB allocated; 0ms collecting garbage
Counts
9 → 12
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((+ (* x (+ x x)) -1) 1 (+ (* x (+ x x)) -1) (* (* x x) 1) (* x x) x (- (* (* x x) 2) 1) (* x (+ x x)) 2)
1.0ms
x
@-inf
((+ (* x (+ x x)) -1) 1 (+ (* x (+ x x)) -1) (* (* x x) 1) (* x x) x (- (* (* x x) 2) 1) (* x (+ x x)) 2)
0.0ms
x
@0
((+ (* x (+ x x)) -1) 1 (+ (* x (+ x x)) -1) (* (* x x) 1) (* x x) x (- (* (* x x) 2) 1) (* x (+ x x)) 2)

rewrite51.0ms (5%)

Memory
-29.2MiB live, 66.6MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035197
038159
114355
0117255
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
21 → 25
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Outputs
#s(approx (- (* (* x x) 2) 1) x)
x
#s(literal 1 binary64)
#s(approx (- (* (* x x) 2) 1) x)
x
#s(literal 1 binary64)
x
#s(literal 1 binary64)
x
#s(literal 1 binary64)
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (* x (+ x x)) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) x)

eval6.0ms (0.6%)

Memory
10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 40 to 17 computations (57.5% saved)

prune1.0ms (0.1%)

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

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New224
Fresh000
Picked213
Done033
Total4610
Accuracy
100.0%
Counts
10 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
52.1%
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
2.9%
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
4.6%
#s(approx (- (* (* x x) 2) 1) x)
49.2%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
25.5%
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
Compiler

Compiled 65 to 47 computations (27.7% saved)

series3.0ms (0.3%)

Memory
9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Counts
5 → 11
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
x
#s(approx (- (* (* x x) 2) 1) x)
Outputs
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((+ (* x (+ x x)) -1) (* (* x x) x) (* x x) x (- (* (* x x) 2) 1))
1.0ms
x
@inf
((+ (* x (+ x x)) -1) (* (* x x) x) (* x x) x (- (* (* x x) 2) 1))
1.0ms
x
@0
((+ (* x (+ x x)) -1) (* (* x x) x) (* x x) x (- (* (* x x) 2) 1))

rewrite95.0ms (9.3%)

Memory
2.8MiB live, 94.4MiB allocated; 12ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
034162
036152
114464
0101564
Stop Event
iter-limit
iter-limit
iter-limit
unsound
iter-limit
Counts
16 → 45
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
x
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
Outputs
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
(*.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 (*.f64 (neg.f64 x) x) (neg.f64 x))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) x))
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) 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))))
(*.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) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 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))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(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))))
x
#s(approx (+ (* x (+ x x)) -1) x)
#s(approx (+ (* x (+ x x)) -1) #s(literal -1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (* (* x x) x) (*.f64 (*.f64 x x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ (* x (+ x x)) -1) #s(literal -1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 2 binary64))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 #s(literal 1 binary64) x) x))
#s(approx (+ (* x (+ x x)) -1) #s(literal 2 binary64))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 #s(literal 1 binary64) x) x))

eval4.0ms (0.4%)

Memory
9.4MiB live, 9.4MiB allocated; 0ms collecting garbage
Compiler

Compiled 579 to 132 computations (77.2% saved)

prune3.0ms (0.3%)

Memory
9.7MiB live, 9.7MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New40040
Fresh000
Picked022
Done044
Total40646
Accuracy
100.0%
Counts
46 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
52.1%
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
2.9%
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
4.6%
#s(approx (- (* (* x x) 2) 1) x)
49.2%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
25.5%
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
Compiler

Compiled 159 to 76 computations (52.2% saved)

regimes15.0ms (1.5%)

Memory
-13.2MiB live, 33.3MiB allocated; 4ms collecting garbage
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Outputs
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
Calls

4 calls:

7.0ms
x
3.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
3.0ms
(*.f64 x x)
3.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
100.0%1(*.f64 x x)
100.0%1(*.f64 (*.f64 x x) #s(literal 2 binary64))
100.0%1(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
100.0%1x
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes20.0ms (1.9%)

Memory
-21.0MiB live, 37.7MiB allocated; 9ms collecting garbage
Counts
7 → 2
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* x (+ x x)) -1) (*.f64 (*.f64 x x) x))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (*.f64 x (+.f64 x x)))
Calls

4 calls:

8.0ms
(*.f64 x x)
7.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
2.0ms
x
2.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
99.5%2(*.f64 x x)
99.5%2(*.f64 (*.f64 x x) #s(literal 2 binary64))
99.5%2(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
99.5%2x
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.7%)

Memory
19.6MiB live, 19.6MiB allocated; 0ms collecting garbage
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) x)
#s(approx (- (* (* x x) 2) 1) #s(approx (* x (+ x x)) #s(literal 2 binary64)))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) x)
Calls

4 calls:

2.0ms
x
2.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
2.0ms
(*.f64 x x)
1.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
52.2%2(*.f64 x x)
52.2%2(*.f64 (*.f64 x x) #s(literal 2 binary64))
52.2%2(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
52.2%2x
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.6%)

Memory
-32.1MiB live, 15.7MiB allocated; 2ms collecting garbage
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
Calls

4 calls:

2.0ms
(*.f64 x x)
1.0ms
x
1.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
1.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
50.9%2(*.f64 x x)
50.9%2(*.f64 (*.f64 x x) #s(literal 2 binary64))
50.9%2(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
50.9%2x
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes4.0ms (0.4%)

Memory
12.7MiB live, 12.7MiB 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) #s(literal 1 binary64))
Outputs
#s(approx (+ (* x (+ x x)) -1) #s(literal 1 binary64))
Calls

4 calls:

1.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
1.0ms
x
1.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
2.9%1(*.f64 x x)
2.9%1(*.f64 (*.f64 x x) #s(literal 2 binary64))
2.9%1(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
2.9%1x
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch10.0ms (1%)

Memory
20.3MiB live, 20.3MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
9.0ms
3.6863610841665176e-7
0.7230844297704999
Samples
4.0ms144×0valid
Compiler

Compiled 208 to 181 computations (13% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-mult!: 1.0ms (62.2% of total)
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)

bsearch1.0ms (0.1%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
1.0ms
3.6863610841665176e-7
0.7230844297704999
Compiler

Compiled 172 to 163 computations (5.2% saved)

bsearch1.0ms (0.1%)

Memory
1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
1.0ms
3.6863610841665176e-7
0.7230844297704999
Compiler

Compiled 172 to 163 computations (5.2% saved)

derivations24.0ms (2.4%)

Memory
-4.5MiB live, 42.9MiB allocated; 2ms collecting garbage
Stop Event
done
Compiler

Compiled 85 to 24 computations (71.8% saved)

preprocess36.0ms (3.6%)

Memory
-3.4MiB live, 93.0MiB allocated; 5ms collecting garbage
Remove

(abs x)

Compiler

Compiled 354 to 168 computations (52.5% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...