Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

Time bar (total: 2.8s)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×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)

sample974.0ms (34.7%)

Memory
0.1MiB live, 1 086.1MiB allocated; 216ms collecting garbage
Samples
599.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 286.0ms
ival-mult: 165.0ms (57.7% of total)
ival-sub: 101.0ms (35.3% of total)
exact: 9.0ms (3.1% of total)
ival-true: 6.0ms (2.1% of total)
ival-assert: 3.0ms (1% of total)
adjust: 2.0ms (0.7% of total)
Bogosity

explain121.0ms (4.3%)

Memory
30.1MiB live, 127.1MiB allocated; 25ms 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
72.0ms512×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 7.0ms (61.8% of total)
ival-sub: 3.0ms (26.5% of total)
exact: 1.0ms (8.8% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess180.0ms (6.4%)

Memory
-12.0MiB live, 222.8MiB allocated; 73ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
12315
27315
321215
471014
5348814
067
097
1197
2567
32027
46607
540367
085356
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Outputs
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% 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
1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify142.0ms (5%)

Memory
-5.1MiB live, 203.5MiB allocated; 27ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal 2 binary64))
cost-diff1
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
0918
11918
25618
320218
466018
5403618
0853517
Stop Event
1×iter limit
1×node limit
1×iter limit
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
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)

localize35.0ms (1.3%)

Memory
-9.1MiB live, 36.6MiB allocated; 3ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
accuracy0.0
(*.f64 x x)
accuracy0.00390625
(*.f64 (*.f64 x x) #s(literal 2 binary64))
Samples
30.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-mult: 23.0ms (93.9% of total)
ival-sub: 1.0ms (4.1% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Counts
3 → 5
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)
Outputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (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))
1.0ms
x
@-inf
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))
1.0ms
x
@0
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))

simplify143.0ms (5.1%)

Memory
-3.8MiB live, 137.9MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
11727
24927
317727
489927
5715927
0815926
Stop Event
1×iter limit
1×node limit
Counts
5 → 5
Calls
Call 1
Inputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
Outputs
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)

rewrite49.0ms (1.8%)

Memory
-1.8MiB live, 43.5MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
13415
023414
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
3 → 60
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)
Outputs
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 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 (*.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 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64) #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 (*.f64 x x) #s(literal 2 binary64) #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 #s(literal 2 binary64) x) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 3 binary64)) (+.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64)))))
(-.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+.f64 (*.f64 #s(literal 2 binary64) (*.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 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x x)))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(*.f64 x (*.f64 #s(literal 2 binary64) 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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) 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 #s(literal 1 binary64) (*.f64 x x) (*.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 x x (*.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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval7.0ms (0.2%)

Memory
14.0MiB live, 14.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 693 to 168 computations (75.8% saved)

prune2.0ms (0.1%)

Memory
4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New63265
Fresh000
Picked101
Done000
Total64266
Accuracy
100.0%
Counts
66 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
▶50.9%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify127.0ms (4.5%)

Memory
3.7MiB live, 192.8MiB allocated; 31ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
cost-diff0
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01022
01322
12422
27022
326721
484621
5382721
0817121
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal -1 binary64)

localize66.0ms (2.4%)

Memory
9.5MiB live, 109.2MiB allocated; 18ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
accuracy0.0
(*.f64 x x)
accuracy31.40477586776202
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Samples
15.0ms256×0valid
Compiler

Compiled 23 to 10 computations (56.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 6.0ms (67.9% of total)
ival-sub: 1.0ms (11.3% of total)
ival-add: 1.0ms (11.3% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
-42.3MiB live, 4.7MiB allocated; 4ms collecting garbage
Counts
3 → 5
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)
Outputs
-1
(- (* 2 (pow x 2)) 1)
(pow x 2)
(* 2 (pow x 2))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
((- (* (* x x) 2) 1) (+ (* (* x x) 2) -1) (* x x))
0.0ms
x
@-inf
((- (* (* x x) 2) 1) (+ (* (* x x) 2) -1) (* x x))
0.0ms
x
@0
((- (* (* x x) 2) 1) (+ (* (* x x) 2) -1) (* x x))

simplify113.0ms (4%)

Memory
34.8MiB live, 81.6MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
11727
24927
317727
489927
5715227
0815226
Stop Event
1×iter limit
1×node limit
Counts
5 → 5
Calls
Call 1
Inputs
-1
(- (* 2 (pow x 2)) 1)
(pow x 2)
(* 2 (pow x 2))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
Outputs
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* 2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)

rewrite63.0ms (2.2%)

Memory
-9.3MiB live, 36.4MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01018
01318
14817
033617
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
3 → 46
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(*.f64 x x)
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64))) (neg.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal -2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (+.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -2 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 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -2 binary64)) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2 binary64)) #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 #s(literal 2 binary64) x) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (*.f64 x x)) #s(literal 2 binary64)))
(-.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 x x)))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) (*.f64 #s(literal 2 binary64) x)))
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -2 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) #s(literal -2 binary64)))))
(+.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal 2 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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval5.0ms (0.2%)

Memory
10.3MiB live, 10.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 602 to 128 computations (78.7% saved)

prune2.0ms (0.1%)

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

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New49150
Fresh000
Picked022
Done000
Total49352
Accuracy
100.0%
Counts
52 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
▶50.3%
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
✓50.9%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify190.0ms (6.8%)

Memory
-39.9MiB live, 86.8MiB allocated; 99ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal 2 binary64))
cost-diff0
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
01123
12123
25823
320423
466623
5404523
0854822
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
Outputs
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)

localize16.0ms (0.6%)

Memory
12.9MiB live, 12.9MiB allocated; 0ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.00390625
(*.f64 (*.f64 x x) #s(literal 2 binary64))
accuracy31.798677460662574
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
Samples
10.0ms256×0valid
Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (58.8% of total)
ival-sub: 1.0ms (19.6% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Counts
3 → 5
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
Outputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (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))
1.0ms
x
@-inf
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))
0.0ms
x
@0
((- (* (* x x) 2) 1) (* (* x x) 2) (* x x))

simplify133.0ms (4.7%)

Memory
-10.3MiB live, 78.4MiB allocated; 12ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
11727
24927
317727
489927
5715227
0815226
Stop Event
1×iter limit
1×node limit
Counts
5 → 5
Calls
Call 1
Inputs
-1
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(pow x 2)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
Outputs
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)

rewrite55.0ms (2%)

Memory
-10.9MiB live, 45.5MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
01121
13621
023620
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
3 → 41
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
Outputs
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 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 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.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 #s(literal 2 binary64) 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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) 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 #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 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval5.0ms (0.2%)

Memory
12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Compiler

Compiled 712 to 133 computations (81.3% saved)

prune4.0ms (0.1%)

Memory
10.7MiB live, 10.7MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New46046
Fresh000
Picked011
Done022
Total46349
Accuracy
100.0%
Counts
49 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
✓50.3%
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
✓50.9%
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes10.0ms (0.4%)

Memory
-24.0MiB live, 21.5MiB allocated; 5ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Outputs
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
Calls

4 calls:

3.0ms
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
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)

regimes5.0ms (0.2%)

Memory
15.6MiB live, 15.6MiB allocated; 0ms collecting garbage
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
Calls

4 calls:

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))
1.0ms
(*.f64 x x)
Results
AccuracySegmentsBranch
99.4%2(*.f64 x x)
99.4%2(*.f64 (*.f64 x x) #s(literal 2 binary64))
99.4%2(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
99.4%2x
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.2%)

Memory
-31.8MiB live, 14.3MiB allocated; 4ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Calls

4 calls:

3.0ms
(*.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%1(*.f64 x x)
50.9%1(*.f64 (*.f64 x x) #s(literal 2 binary64))
50.9%1(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
50.9%1x
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch12.0ms (0.4%)

Memory
26.5MiB live, 26.5MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
11.0ms
0.12886321219464955
28473.366371047636
Samples
6.0ms144×0valid
Compiler

Compiled 208 to 190 computations (8.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 2.0ms (69.6% of total)
ival-sub: 1.0ms (34.8% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify56.0ms (2%)

Memory
18.2MiB live, 65.0MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01541
12541
26241
321741
4109341
5445741
Stop Event
1×node limit
Calls
Call 1
Inputs
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(if (<=.f64 x #s(literal 3152519739159347/4503599627370496 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64))))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Outputs
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(if (<=.f64 x #s(literal 3152519739159347/4503599627370496 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64))))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

derivations240.0ms (8.6%)

Memory
-48.1MiB live, 194.7MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
11727
24927
317727
489927
5715227
0815226
0615
0915
13415
023414
01027
11727
24927
317727
489927
5715927
0815926
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 41 to 16 computations (61% saved)

preprocess35.0ms (1.2%)

Memory
1.4MiB live, 47.1MiB allocated; 4ms collecting garbage
Remove

(abs x)

Compiler

Compiled 108 to 54 computations (50% saved)

end0.0ms (0%)

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

Profiling

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