Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

Time bar (total: 2.2s)

start0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB 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)

sample781.0ms (35%)

Memory
-30.1MiB live, 1 067.0MiB allocated; 281ms collecting garbage
Samples
499.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 225.0ms
ival-mult: 168.0ms (74.8% of total)
ival-sub: 42.0ms (18.7% of total)
exact: 9.0ms (4% of total)
adjust: 2.0ms (0.9% of total)
ival-assert: 2.0ms (0.9% of total)
Bogosity

explain71.0ms (3.2%)

Memory
18.0MiB live, 119.1MiB allocated; 17ms 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
22.0ms512×0valid
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 (64.3% of total)
ival-sub: 2.0ms (18.4% of total)
exact: 1.0ms (9.2% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess187.0ms (8.4%)

Memory
31.4MiB live, 162.6MiB allocated; 38ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
12922
28322
323722
475721
5387821
067
097
1197
2567
32027
46607
540367
085356
Stop Event
iter limit
node limit
iter limit
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
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB 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)

simplify174.0ms (7.8%)

Memory
-2.7MiB live, 186.1MiB allocated; 35ms 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
iter limit
node limit
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)

localize32.0ms (1.4%)

Memory
-1.1MiB live, 52.4MiB allocated; 12ms 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)
accuracy0.01171875
(*.f64 (*.f64 x x) #s(literal 2 binary64))
Samples
27.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 19.0ms (89.8% of total)
ival-sub: 1.0ms (4.7% 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)

series5.0ms (0.2%)

Memory
-40.2MiB live, 5.8MiB allocated; 5ms collecting garbage
Counts
3 → 6
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
#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 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
3.0ms
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))

simplify249.0ms (11.2%)

Memory
-13.4MiB live, 244.2MiB allocated; 124ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01974
13474
210674
334474
4129974
5703674
0807969
Stop Event
iter limit
node limit
Counts
6 → 6
Calls
Call 1
Inputs
#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 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) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (- (* (* x x) 2) 1) (fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* (* x x) 2) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x))

rewrite46.0ms (2.1%)

Memory
2.8MiB live, 107.2MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
13415
023414
Stop Event
iter limit
iter limit
iter limit
unsound
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 (0.3%)

Memory
27.6MiB live, 27.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 706 to 169 computations (76.1% saved)

prune14.0ms (0.6%)

Memory
-35.5MiB live, 9.0MiB allocated; 5ms collecting garbage
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New63366
Fresh000
Picked101
Done000
Total64367
Accuracy
100.0%
Counts
67 → 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))
49.3%
#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)

simplify148.0ms (6.7%)

Memory
31.9MiB live, 175.0MiB allocated; 13ms collecting garbage
Localize:

Found 6 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
(*.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)))
cost-diff0
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01245
01545
12645
27245
327243
484743
5383343
0818043
Stop Event
iter limit
node limit
iter limit
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 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 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)
#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)
(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)

localize33.0ms (1.5%)

Memory
2.8MiB live, 47.1MiB allocated; 4ms collecting garbage
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
accuracy0.0
(*.f64 x x)
accuracy0.0
(*.f64 x x)
accuracy0.01171875
(*.f64 (*.f64 x x) #s(literal 2 binary64))
accuracy32.43870975663325
#s(approx (- (* (* x x) 2) 1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
accuracy31.44272117334677
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Samples
27.0ms256×0valid
Compiler

Compiled 40 to 10 computations (75% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-mult: 16.0ms (81.2% of total)
ival-sub: 1.0ms (5.1% of total)
ival-add: 1.0ms (5.1% 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
5.1MiB live, 5.1MiB allocated; 0ms collecting garbage
Counts
5 → 10
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)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
(fma.f64 (*.f64 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 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) 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) 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) 1) (* (* x x) 2) (* x x) (+ (* (* x x) 2) -1))
1.0ms
x
@-inf
((- (* (* x x) 2) 1) (- (* (* x x) 2) 1) (* (* x x) 2) (* x x) (+ (* (* x x) 2) -1))
0.0ms
x
@0
((- (* (* x x) 2) 1) (- (* (* x x) 2) 1) (* (* x x) 2) (* x x) (+ (* (* x x) 2) -1))

simplify210.0ms (9.4%)

Memory
-17.1MiB live, 126.8MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024130
143130
2128130
3437130
41522130
57500130
08487120
Stop Event
iter limit
node limit
Counts
10 → 10
Calls
Call 1
Inputs
#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 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) 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) 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) #s(hole binary64 -1))
#s(approx (+ (* (* x x) 2) -1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (+ (* (* x x) 2) -1) (fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* (* x x) 2) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* x x) 2) -1) #s(hole binary64 -1))
#s(approx (+ (* (* x x) 2) -1) #s(literal -1 binary64))
#s(approx (+ (* (* x x) 2) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (+ (* (* x x) 2) -1) (fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* (* x x) 2) -1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (+ (* (* x x) 2) -1) (*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x))
#s(approx (+ (* (* x x) 2) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* (* x x) 2) -1) (*.f64 (*.f64 x x) #s(literal 2 binary64)))
#s(approx (+ (* (* x x) 2) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (+ (* (* x x) 2) -1) (*.f64 (*.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x))

rewrite47.0ms (2.1%)

Memory
8.1MiB live, 50.8MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01236
01536
15034
033834
Stop Event
iter limit
iter limit
iter limit
unsound
iter limit
Counts
5 → 73
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)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 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)))
(*.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 (*.f64 (*.f64 x x) #s(literal -2 binary64)) #s(literal -1 binary64))
(*.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)))
(/.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)))

eval14.0ms (0.6%)

Memory
-16.7MiB live, 26.7MiB allocated; 9ms collecting garbage
Compiler

Compiled 1 296 to 215 computations (83.4% saved)

prune4.0ms (0.2%)

Memory
14.4MiB live, 14.4MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New95095
Fresh000
Picked033
Done000
Total95398
Accuracy
100.0%
Counts
98 → 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))
49.3%
#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)

regimes7.0ms (0.3%)

Memory
19.7MiB live, 19.7MiB allocated; 0ms 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:

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
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)

regimes9.0ms (0.4%)

Memory
-31.3MiB live, 14.2MiB allocated; 7ms 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:

5.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
1.0ms
x
1.0ms
(*.f64 x x)
1.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
98.4%2(*.f64 x x)
98.4%2(*.f64 (*.f64 x x) #s(literal 2 binary64))
98.4%2(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
98.4%2x
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes4.0ms (0.2%)

Memory
12.2MiB live, 12.2MiB 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) 2) 1) #s(literal -1 binary64))
Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
Calls

4 calls:

1.0ms
x
1.0ms
(-.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
1.0ms
(*.f64 (*.f64 x x) #s(literal 2 binary64))
1.0ms
(*.f64 x x)
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)

bsearch10.0ms (0.4%)

Memory
21.2MiB live, 21.2MiB allocated; 0ms collecting garbage
Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
8.0ms
0.4916708481587397
94.36781108304396
Samples
4.0ms112×0valid
Compiler

Compiled 164 to 150 computations (8.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-sub: 1.0ms (45.2% of total)
ival-mult: 1.0ms (45.2% 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)

simplify67.0ms (3%)

Memory
-27.9MiB live, 75.6MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01541
12541
26241
321741
4109341
5445741
Stop Event
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))

derivations82.0ms (3.7%)

Memory
-10.1MiB live, 81.6MiB allocated; 12ms collecting garbage
Stop Event
done
Compiler

Compiled 41 to 16 computations (61% saved)

preprocess26.0ms (1.2%)

Memory
9.1MiB live, 58.2MiB allocated; 13ms 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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