Data.Random.Distribution.Normal:doubleStdNormalZ from random-fu-0.2.6.2

Time bar (total: 1.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 7 to 6 computations (14.3% saved)

sample531.0ms (38.2%)

Memory
50.1MiB live, 466.4MiB allocated
Samples
287.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 108.0ms
ival-add: 54.0ms (49.9% of total)
ival-sub: 41.0ms (37.9% of total)
ival-true: 5.0ms (4.6% of total)
exact: 5.0ms (4.6% of total)
ival-assert: 3.0ms (2.8% of total)
Bogosity

explain69.0ms (5%)

Memory
-26.0MiB live, 58.1MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(+.f64 x x)
00-0-#s(literal 1 binary64)
00-0-(-.f64 (+.f64 x x) #s(literal 1 binary64))
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
34.0ms512×0valid
Compiler

Compiled 30 to 16 computations (46.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-add: 3.0ms (51.4% of total)
ival-sub: 2.0ms (34.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess30.0ms (2.1%)

Memory
-6.9MiB live, 31.5MiB allocated
Algorithm
1×egg-herbie
Rules
88×lower-fma.f64
88×lower-fma.f32
40×lower-*.f64
40×lower-*.f32
30×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
12211
27210
317410
425210
526510
045
065
1155
2195
3245
4285
5375
6665
71485
82325
92465
102485
02484
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Outputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))
Compiler

Compiled 6 to 4 computations (33.3% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify10.0ms (0.7%)

Memory
10.9MiB live, 10.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x x)
cost-diff0
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Rules
88×lower-fma.f64
88×lower-fma.f32
40×lower-*.f64
40×lower-*.f32
30×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0410
0610
11510
21910
32410
42810
53710
66610
714810
823210
924610
1024810
02489
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(+.f64 x x)
x
#s(literal 1 binary64)
Outputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))
(+.f64 x x)
x
#s(literal 1 binary64)

localize12.0ms (0.9%)

Memory
21.1MiB live, 21.1MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 (+.f64 x x) #s(literal 1 binary64))
accuracy0
(+.f64 x x)
Samples
7.0ms256×0valid
Compiler

Compiled 12 to 6 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sub: 1.0ms (36.2% of total)
ival-add: 1.0ms (36.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
2.9MiB live, 2.9MiB allocated
Counts
2 → 24
Calls
Call 1
Inputs
#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt (-.f64 (+.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (+.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify19.0ms (1.4%)

Memory
-31.1MiB live, 7.3MiB allocated
Algorithm
1×egg-herbie
Rules
60×lower-fma.f64
60×lower-fma.f32
42×lower-*.f64
42×lower-*.f32
28×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01288
12888
26388
311888
413288
518688
622788
725288
826788
927388
1027488
027479
Stop Event
1×iter limit
1×saturated
Counts
24 → 24
Calls
Call 1
Inputs
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
Outputs
-1
#s(literal -1 binary64)
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))

rewrite147.0ms (10.6%)

Memory
-22.5MiB live, 38.1MiB allocated
Rules
776×frac-times
442×frac-sub
208×frac-add
111×associate-*l/
109×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
0610
13610
230310
3531810
0610
13610
230310
068
1368
03037
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
2 → 69
Calls
Call 1
Inputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(+.f64 x x)
Outputs
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))) (-.f64 x (-.f64 x #s(literal 1 binary64))))
(/.f64 (fma.f64 (*.f64 x x) x (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 2 binary64) x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)) (-.f64 (+.f64 x x) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x x) #s(literal -1 binary64)))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))))
(fma.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal 4 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x (+.f64 x x)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) x #s(literal -1 binary64))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (+.f64 x x) #s(literal -1 binary64))
(fma.f64 (+.f64 x x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (+.f64 x x) (+.f64 x x) #s(literal -1 binary64))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(expm1.f64 (*.f64 (log.f64 (+.f64 x x)) #s(literal 3 binary64)))
(-.f64 (/.f64 (+.f64 x x) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(-.f64 (/.f64 (+.f64 x x) (fma.f64 #s(literal 2 binary64) x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(+.f64 (-.f64 x #s(literal 1 binary64)) x)
(+.f64 #s(literal -1 binary64) (+.f64 x x))
(+.f64 (+.f64 x x) #s(literal -1 binary64))
(+.f64 x (-.f64 x #s(literal 1 binary64)))
(*.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64)) x)
(*.f64 #s(literal 4 binary64) (*.f64 x x))
(*.f64 (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)))
(*.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))
(*.f64 #s(literal 2 binary64) (*.f64 x (+.f64 x x)))
(*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 x x))
(*.f64 (+.f64 x x) #s(literal 1 binary64))
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x x) #s(literal 2 binary64))
(pow.f64 (+.f64 x x) #s(literal 3 binary64))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 0 binary64) (+.f64 x x)) #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (+.f64 x x) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 x x))
(fma.f64 (+.f64 x x) x (*.f64 (+.f64 x x) x))
(fma.f64 x (+.f64 x x) (*.f64 x (+.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) #s(literal 3 binary64)))
(+.f64 (*.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x)))
(+.f64 (*.f64 (+.f64 x x) x) (*.f64 (+.f64 x x) x))
(+.f64 x x)

eval9.0ms (0.6%)

Memory
12.6MiB live, 12.6MiB allocated
Compiler

Compiled 881 to 165 computations (81.3% saved)

prune12.0ms (0.8%)

Memory
18.9MiB live, 18.9MiB allocated
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New91293
Fresh000
Picked011
Done000
Total91394
Accuracy
100.0%
Counts
94 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(-.f64 (+.f64 x x) #s(literal 1 binary64))
▶52.8%
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
▶48.6%
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify34.0ms (2.5%)

Memory
-31.6MiB live, 8.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
cost-diff128
(*.f64 x #s(literal 2 binary64))
cost-diff0
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
Rules
88×lower-fma.f64
88×lower-fma.f32
40×lower-*.f32
39×lower-*.f64
30×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0922
01022
11822
22122
32622
43022
53922
66822
715022
823422
924822
1025022
025020
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
Outputs
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
#s(approx (- (+ x x) 1) (+.f64 x x))
(*.f64 x #s(literal 2 binary64))
(+.f64 x x)
x
#s(literal 2 binary64)

localize17.0ms (1.2%)

Memory
32.9MiB live, 32.9MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x #s(literal 2 binary64))
accuracy30.234353493894137
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
accuracy32.88441968016833
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
Samples
10.0ms256×0valid
Compiler

Compiled 18 to 9 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 2.0ms (42.7% of total)
ival-sub: 1.0ms (21.3% of total)
ival-add: 1.0ms (21.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
3.6MiB live, 3.6MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
Outputs
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) #s(literal -1 binary64)) (patch #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2 binary64)) (patch (*.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) (patch #s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
Calls

9 calls:

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

simplify24.0ms (1.7%)

Memory
-13.8MiB live, 25.2MiB allocated
Algorithm
1×egg-herbie
Rules
60×lower-fma.f64
60×lower-fma.f32
42×lower-*.f64
42×lower-*.f32
28×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012140
128140
263140
3118140
4132140
5186140
6227140
7252140
8267140
9273140
10274140
0274122
Stop Event
1×iter limit
1×saturated
Counts
36 → 36
Calls
Call 1
Inputs
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
Outputs
-1
#s(literal -1 binary64)
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
-1
#s(literal -1 binary64)
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))

rewrite125.0ms (9%)

Memory
-15.8MiB live, 63.8MiB allocated
Rules
776×frac-times
442×frac-sub
208×frac-add
137×lower-fma.f64
137×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
01017
13917
231317
3544317
01017
13917
231317
01019
13919
031317
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) 1) #s(literal -1 binary64))
(*.f64 x #s(literal 2 binary64))
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
Outputs
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
(*.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64)) x)
(*.f64 (*.f64 (+.f64 x x) x) #s(literal 2 binary64))
(*.f64 #s(literal 4 binary64) (*.f64 x x))
(*.f64 (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)))
(*.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 x x) #s(literal 4 binary64))
(*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (*.f64 (*.f64 x x) x) #s(literal 8 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 x (+.f64 x x)))
(*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 1 binary64) (+.f64 x x))
(*.f64 (+.f64 x x) #s(literal 1 binary64))
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 x (*.f64 #s(literal 2 binary64) (+.f64 x x)))
(*.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x x) #s(literal 3 binary64))
(pow.f64 (+.f64 x x) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) (+.f64 x x)) #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (+.f64 x x) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 x x))
(fma.f64 (+.f64 x x) x (*.f64 (+.f64 x x) x))
(fma.f64 x (+.f64 x x) (*.f64 x (+.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) #s(literal 3 binary64)))
(+.f64 (*.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x)))
(+.f64 (*.f64 (+.f64 x x) x) (*.f64 (+.f64 x x) x))
(+.f64 x x)
#s(approx (- (+ x x) 1) (+.f64 x x))

eval7.0ms (0.5%)

Memory
11.3MiB live, 11.3MiB allocated
Compiler

Compiled 585 to 79 computations (86.5% saved)

prune7.0ms (0.5%)

Memory
11.6MiB live, 11.6MiB allocated
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New76177
Fresh000
Picked112
Done011
Total77380
Accuracy
100.0%
Counts
80 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(-.f64 (+.f64 x x) #s(literal 1 binary64))
▶52.8%
#s(approx (- (+ x x) 1) (+.f64 x x))
✓48.6%
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify78.0ms (5.6%)

Memory
-28.1MiB live, 10.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x x)
cost-diff0
#s(approx (- (+ x x) 1) (+.f64 x x))
Rules
88×lower-fma.f64
88×lower-fma.f32
40×lower-*.f64
40×lower-*.f32
30×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
0713
11613
22013
32513
42913
53813
66713
715013
823413
924813
1025013
025012
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (+ x x) 1) (+.f64 x x))
(+.f64 x x)
x
Outputs
#s(approx (- (+ x x) 1) (+.f64 x x))
(+.f64 x x)
x

localize12.0ms (0.8%)

Memory
23.8MiB live, 23.8MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 x x)
accuracy30.234353493894137
#s(approx (- (+ x x) 1) (+.f64 x x))
Samples
7.0ms256×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sub: 1.0ms (34.9% of total)
ival-add: 1.0ms (34.9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Counts
2 → 24
Calls
Call 1
Inputs
#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 x) 1) (taylor 0 x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 2))) (taylor -inf x) (#s(alt #s(approx (- (+ x x) 1) (+.f64 x x)) (patch #s(approx (- (+ x x) 1) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
Calls

6 calls:

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

simplify12.0ms (0.9%)

Memory
-18.4MiB live, 18.7MiB allocated
Algorithm
1×egg-herbie
Rules
60×lower-fma.f64
60×lower-fma.f32
42×lower-*.f64
42×lower-*.f32
28×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01288
12888
26388
311888
413288
518688
622788
725288
826788
927388
1027488
027479
Stop Event
1×iter limit
1×saturated
Counts
24 → 24
Calls
Call 1
Inputs
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
Outputs
-1
#s(literal -1 binary64)
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(- (* 2 x) 1)
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* x (- 2 (/ 1 x)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 2)))
(fma.f64 x #s(literal 2 binary64) #s(literal -1 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))

rewrite52.0ms (3.8%)

Memory
9.4MiB live, 88.0MiB allocated
Rules
776×frac-times
442×frac-sub
208×frac-add
111×associate-*l/
109×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0612
0712
13712
230512
3532212
0712
13712
230512
0712
13712
030511
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
2 → 36
Calls
Call 1
Inputs
#s(approx (- (+ x x) 1) (+.f64 x x))
(+.f64 x x)
Outputs
#s(approx (- (+ x x) 1) (+.f64 x x))
(*.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64)) x)
(*.f64 #s(literal 4 binary64) (*.f64 x x))
(*.f64 (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 3/2 binary64)))
(*.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))
(*.f64 #s(literal 2 binary64) (*.f64 x (+.f64 x x)))
(*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 (+.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x x))
(*.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x x) #s(literal 2 binary64))
(pow.f64 (+.f64 x x) #s(literal 3 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) (+.f64 x x)) #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (+.f64 x x) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (*.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 x x))
(fma.f64 (+.f64 x x) x (*.f64 (+.f64 x x) x))
(fma.f64 x (+.f64 x x) (*.f64 x (+.f64 x x)))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) #s(literal 3 binary64)))
(+.f64 (*.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x)))
(+.f64 (*.f64 (+.f64 x x) x) (*.f64 (+.f64 x x) x))
(+.f64 x x)

eval6.0ms (0.4%)

Memory
17.3MiB live, 17.3MiB allocated
Compiler

Compiled 498 to 74 computations (85.1% saved)

prune10.0ms (0.7%)

Memory
-20.7MiB live, 17.2MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New60060
Fresh000
Picked011
Done022
Total60363
Accuracy
100.0%
Counts
63 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(-.f64 (+.f64 x x) #s(literal 1 binary64))
✓52.8%
#s(approx (- (+ x x) 1) (+.f64 x x))
✓48.6%
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
Compiler

Compiled 30 to 15 computations (50% saved)

regimes6.0ms (0.5%)

Memory
13.8MiB live, 13.8MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
#s(approx (- (+ x x) 1) (+.f64 x x))
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Outputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Calls

3 calls:

2.0ms
(+.f64 x x)
2.0ms
x
2.0ms
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (+.f64 x x) #s(literal 1 binary64))
100.0%1(+.f64 x x)
Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes5.0ms (0.4%)

Memory
11.0MiB live, 11.0MiB allocated
Counts
3 → 3
Calls
Call 1
Inputs
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
#s(approx (- (+ x x) 1) (+.f64 x x))
#s(approx (- (+ x x) 1) (*.f64 x #s(literal 2 binary64)))
Outputs
#s(approx (- (+ x x) 1) (+.f64 x x))
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
#s(approx (- (+ x x) 1) (+.f64 x x))
Calls

3 calls:

2.0ms
(+.f64 x x)
2.0ms
x
2.0ms
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
97.9%3x
97.9%3(-.f64 (+.f64 x x) #s(literal 1 binary64))
97.9%3(+.f64 x x)
Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes13.0ms (0.9%)

Memory
-26.7MiB live, 11.1MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

3 calls:

10.0ms
x
1.0ms
(+.f64 x x)
1.0ms
(-.f64 (+.f64 x x) #s(literal 1 binary64))
Results
AccuracySegmentsBranch
48.6%1x
48.6%1(-.f64 (+.f64 x x) #s(literal 1 binary64))
48.6%1(+.f64 x x)
Compiler

Compiled 12 to 7 computations (41.7% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
2.8282008227588642e-9
783608.4016971984
0.0ms
-15.046154357056677
-0.0009664654482849371
Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify6.0ms (0.4%)

Memory
12.2MiB live, 12.2MiB allocated
Algorithm
1×egg-herbie
Rules
2×sub-neg_binary64
1×*-commutative_binary64
1×+-commutative_binary64
1×mul-1-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01549
12049
22349
32749
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(if (<=.f64 (+.f64 x x) #s(literal -10 binary64)) #s(approx (- (+ x x) 1) (+.f64 x x)) (if (<=.f64 (+.f64 x x) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #s(approx (- (+ x x) 1) (+.f64 x x))))
#s(approx (- (+ x x) 1) #s(literal -1 binary64))
Outputs
(-.f64 (+.f64 x x) #s(literal 1 binary64))
(if (<=.f64 (+.f64 x x) #s(literal -10 binary64)) #s(approx (- (+ x x) 1) (+.f64 x x)) (if (<=.f64 (+.f64 x x) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (- (+ x x) 1) #s(literal -1 binary64)) #s(approx (- (+ x x) 1) (+.f64 x x))))
#s(approx (- (+ x x) 1) #s(literal -1 binary64))

soundness64.0ms (4.6%)

Memory
14.2MiB live, 52.1MiB allocated
Rules
776×frac-times
442×frac-sub
208×frac-add
137×lower-fma.f64
137×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
01017
13917
231317
3544317
01017
13917
231317
01019
13919
031317
01288
12888
26388
311888
413288
518688
622788
725288
826788
927388
1027488
027479
Stop Event
1×done
1×iter limit
1×saturated
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Compiler

Compiled 43 to 21 computations (51.2% saved)

preprocess66.0ms (4.7%)

Memory
-19.2MiB live, 60.8MiB allocated
Compiler

Compiled 72 to 30 computations (58.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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