Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

Time bar (total: 1.9s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 9 to 9 computations (0% saved)

sample496.0ms (26.2%)

Memory
191.4MiB live, 191.4MiB allocated
Samples
298.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 143.0ms
ival-mult: 96.0ms (67.1% of total)
ival-sub: 34.0ms (23.8% of total)
ival-true: 5.0ms (3.5% of total)
exact: 4.0ms (2.8% of total)
ival-assert: 3.0ms (2.1% of total)
Bogosity

explain80.0ms (4.2%)

Memory
40.3MiB live, 40.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-y
00-0-(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
00-0-(*.f64 y #s(literal 4 binary64))
00-0-#s(literal 4 binary64)
00-0-z
00-0-(*.f64 (*.f64 y #s(literal 4 binary64)) z)
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
23.0ms512×0valid
Compiler

Compiled 106 to 58 computations (45.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 6.0ms (64.6% of total)
ival-sub: 2.0ms (21.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess40.0ms (2.1%)

Memory
7.4MiB live, 7.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02669
19266
224163
355963
490463
599863
6101263
7101263
8101263
077
0107
1197
2497
3997
41317
51707
62217
72637
83487
94007
104307
04306
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
Outputs
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
(fma.f64 (*.f64 z y) #s(literal -4 binary64) x)
Symmetry

(sort y z)

Compiler

Compiled 7 to 7 computations (0% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
Compiler

Compiled 7 to 7 computations (0% saved)

simplify12.0ms (0.6%)

Memory
1.4MiB live, 1.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 y #s(literal 4 binary64))
cost-diff0
(*.f64 (*.f64 y #s(literal 4 binary64)) z)
cost-diff128
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0719
01019
11919
24919
39919
413119
517019
622119
726319
834819
940019
1043019
043018
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
x
(*.f64 (*.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
z
Outputs
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
(fma.f64 (*.f64 z y) #s(literal -4 binary64) x)
x
(*.f64 (*.f64 y #s(literal 4 binary64)) z)
(*.f64 z (*.f64 #s(literal 4 binary64) y))
(*.f64 y #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) y)
y
#s(literal 4 binary64)
z

localize15.0ms (0.8%)

Memory
7.0MiB live, 7.0MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 (*.f64 y #s(literal 4 binary64)) z)
accuracy0
(*.f64 y #s(literal 4 binary64))
accuracy0.00390625
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
Samples
11.0ms256×0valid
Compiler

Compiled 40 to 16 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-mult: 3.0ms (66.8% of total)
ival-sub: 1.0ms (22.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series7.0ms (0.4%)

Memory
3.2MiB live, 3.2MiB allocated
Counts
3 → 72
Calls
Call 1
Inputs
#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())
#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (* 4 y))) (taylor inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (* 4 y))) (taylor inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (* 4 y))) (taylor inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ x z)) (* -4 y)))) (taylor -inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ x z)) (* -4 y)))) (taylor -inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ x z)) (* -4 y)))) (taylor -inf z) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) (* 4 z))) (taylor inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) (* 4 z))) (taylor inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) (* 4 z))) (taylor inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) (* -4 z)))) (taylor -inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) (* -4 z)))) (taylor -inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) (* -4 z)))) (taylor -inf y) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (*.f64 (*.f64 y #s(literal 4 binary64)) z) (patch (*.f64 (*.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (*.f64 y #s(literal 4 binary64)) (patch (*.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (- x (* 4 (* y z))) (taylor 0 x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (- x (* 4 (* y z))) (taylor 0 x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (- x (* 4 (* y z))) (taylor 0 x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -4 (/ (* y z) x)))) (taylor inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -4 (/ (* y z) x)))) (taylor inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -4 (/ (* y z) x)))) (taylor inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
1.0ms
y
@-inf
((- x (* (* y 4) z)) (* (* y 4) z) (* y 4))
1.0ms
y
@0
((- x (* (* y 4) z)) (* (* y 4) z) (* y 4))
1.0ms
y
@inf
((- x (* (* y 4) z)) (* (* y 4) z) (* y 4))
1.0ms
z
@inf
((- x (* (* y 4) z)) (* (* y 4) z) (* y 4))
1.0ms
z
@0
((- x (* (* y 4) z)) (* (* y 4) z) (* y 4))

simplify163.0ms (8.6%)

Memory
35.5MiB live, 35.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038374
1105374
2262374
3894374
42564374
54474374
65491374
75869374
86083374
96195374
106237374
08299347
Stop Event
iter limit
node limit
Counts
72 → 68
Calls
Call 1
Inputs
x
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* -4 (* y z))
(* z (- (/ x z) (* 4 y)))
(* z (- (/ x z) (* 4 y)))
(* z (- (/ x z) (* 4 y)))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* -4 (* y z))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
x
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (* y z))
(* y (- (/ x y) (* 4 z)))
(* y (- (/ x y) (* 4 z)))
(* y (- (/ x y) (* 4 z)))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (* y z))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (* y z))
(- x (* 4 (* y z)))
(- x (* 4 (* y z)))
(- x (* 4 (* y z)))
x
(* x (+ 1 (* -4 (/ (* y z) x))))
(* x (+ 1 (* -4 (/ (* y z) x))))
(* x (+ 1 (* -4 (/ (* y z) x))))
x
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
Outputs
x
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* z (- (/ x z) (* 4 y)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* z (- (/ x z) (* 4 y)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* z (- (/ x z) (* 4 y)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
x
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y (- (/ x y) (* 4 z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* y (- (/ x y) (* 4 z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* y (- (/ x y) (* 4 z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 (* y z))
(*.f64 #s(literal 4 binary64) (*.f64 z y))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(- x (* 4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(- x (* 4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(- x (* 4 (* y z)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
x
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
x
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)

rewrite140.0ms (7.4%)

Memory
56.5MiB live, 56.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
01015
13215
221915
3211815
0834014
Stop Event
iter limit
node limit
iter limit
Counts
3 → 207
Calls
Call 1
Inputs
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
(*.f64 (*.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))
Outputs
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eval26.0ms (1.4%)

Memory
23.6MiB live, 23.6MiB allocated
Compiler

Compiled 8 646 to 640 computations (92.6% saved)

prune6.0ms (0.3%)

Memory
11.3MiB live, 11.3MiB allocated
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2732275
Fresh000
Picked101
Done000
Total2742276
Accuracy
100.0%
Counts
276 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
54.9%
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Compiler

Compiled 12 to 13 computations (-8.3% saved)

simplify12.0ms (0.6%)

Memory
1.5MiB live, 1.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -4 binary64) z)
cost-diff0
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
cost-diff0
(*.f64 z y)
cost-diff0
(*.f64 (*.f64 z y) #s(literal -4 binary64))
cost-diff0
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01337
01837
13536
26236
310136
413436
517336
622436
726736
835236
940436
1043436
043436
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(*.f64 z y)
z
y
#s(literal -4 binary64)
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
(*.f64 #s(literal -4 binary64) z)
#s(literal -4 binary64)
z
y
x
Outputs
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 #s(literal -4 binary64) z) y))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(*.f64 (*.f64 #s(literal -4 binary64) z) y)
(*.f64 z y)
(*.f64 y z)
z
y
#s(literal -4 binary64)
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
(fma.f64 #s(literal -4 binary64) (*.f64 y z) x)
(*.f64 #s(literal -4 binary64) z)
#s(literal -4 binary64)
z
y
x

localize26.0ms (1.3%)

Memory
11.6MiB live, 11.6MiB allocated
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
accuracy0
(*.f64 #s(literal -4 binary64) z)
accuracy0
(*.f64 z y)
accuracy0.00390625
(*.f64 (*.f64 z y) #s(literal -4 binary64))
accuracy28.890184312576558
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Samples
19.0ms256×0valid
Compiler

Compiled 64 to 24 computations (62.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 8.0ms (73.3% of total)
ival-sub: 1.0ms (9.2% of total)
ival-add: 1.0ms (9.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series7.0ms (0.4%)

Memory
4.3MiB live, 4.3MiB allocated
Counts
5 → 132
Calls
Call 1
Inputs
#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 z y) #s(literal -4 binary64)) (patch (*.f64 (*.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -4 binary64) z) (patch (*.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())
Outputs
#s(alt x (taylor 0 z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 z y) #s(literal -4 binary64)) (patch (*.f64 (*.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 z y) #s(literal -4 binary64)) (patch (*.f64 (*.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 z y) #s(literal -4 binary64)) (patch (*.f64 (*.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (*.f64 (*.f64 z y) #s(literal -4 binary64)) (patch (*.f64 (*.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (*.f64 z y) (patch (*.f64 z y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 z) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -4 (* y z))) (taylor 0 z) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (*.f64 #s(literal -4 binary64) z) (patch (*.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (*.f64 #s(literal -4 binary64) z) (patch (*.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (*.f64 #s(literal -4 binary64) z) (patch (*.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (*.f64 #s(literal -4 binary64) z) (patch (*.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ x z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
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#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 4 (/ (* y z) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) (patch (fma.f64 (*.f64 #s(literal -4 binary64) z) y x) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
1.0ms
z
@-inf
((- x (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) x) (* -4 z))
1.0ms
z
@0
((- x (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) x) (* -4 z))
1.0ms
y
@-inf
((- x (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) x) (* -4 z))
1.0ms
z
@inf
((- x (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) x) (* -4 z))
0.0ms
y
@inf
((- x (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) x) (* -4 z))

simplify72.0ms (3.8%)

Memory
15.4MiB live, 15.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048664
1143664
2369664
31010664
42673664
55459664
67583664
08102610
Stop Event
iter limit
node limit
Counts
132 → 124
Calls
Call 1
Inputs
x
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
x
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 (* y z))
(* z (- (/ x z) (* 4 y)))
(* z (- (/ x z) (* 4 y)))
(* z (- (/ x z) (* 4 y)))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* z (+ (* -4 y) (/ x z)))
(* z (+ (* -4 y) (/ x z)))
(* z (+ (* -4 y) (/ x z)))
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 (* y z))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* -1 (* z (+ (* -1 (/ x z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ x z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ x z)) (* 4 y))))
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 z)
x
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
x
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(* -4 (* y z))
(* y (- (/ x y) (* 4 z)))
(* y (- (/ x y) (* 4 z)))
(* y (- (/ x y) (* 4 z)))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* y (+ (* -4 z) (/ x y)))
(* y (+ (* -4 z) (/ x y)))
(* y (+ (* -4 z) (/ x y)))
(* -4 (* y z))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* -1 (* y (+ (* -1 (/ x y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ x y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ x y)) (* 4 z))))
(* -4 (* y z))
(- x (* 4 (* y z)))
(- x (* 4 (* y z)))
(- x (* 4 (* y z)))
(* -4 (* y z))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
(+ x (* -4 (* y z)))
x
(* x (+ 1 (* -4 (/ (* y z) x))))
(* x (+ 1 (* -4 (/ (* y z) x))))
(* x (+ 1 (* -4 (/ (* y z) x))))
x
(* x (+ 1 (* -4 (/ (* y z) x))))
(* x (+ 1 (* -4 (/ (* y z) x))))
(* x (+ 1 (* -4 (/ (* y z) x))))
x
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
x
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
Outputs
x
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
x
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* z (- (/ x z) (* 4 y)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* z (- (/ x z) (* 4 y)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* z (- (/ x z) (* 4 y)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* z (+ (* -4 y) (/ x z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* z (+ (* -4 y) (/ x z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* z (+ (* -4 y) (/ x z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* z (- (* -1 (/ x z)) (* -4 y))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -1 (* z (+ (* -1 (/ x z)) (* 4 y))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* z (+ (* -1 (/ x z)) (* 4 y))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* z (+ (* -1 (/ x z)) (* 4 y))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
x
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
x
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y (- (/ x y) (* 4 z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* y (- (/ x y) (* 4 z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* y (- (/ x y) (* 4 z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y (+ (* -4 z) (/ x y)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* y (+ (* -4 z) (/ x y)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* y (+ (* -4 z) (/ x y)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* y (- (* -1 (/ x y)) (* -4 z))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(* -1 (* y (+ (* -1 (/ x y)) (* 4 z))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* y (+ (* -1 (/ x y)) (* 4 z))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* y (+ (* -1 (/ x y)) (* 4 z))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(- x (* 4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(- x (* 4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(- x (* 4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -4 (* y z))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(+ x (* -4 (* y z)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
x
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
x
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* x (+ 1 (* -4 (/ (* y z) x))))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
x
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
x
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)
(* -1 (* x (- (* 4 (/ (* y z) x)) 1)))
(fma.f64 (*.f64 y #s(literal -4 binary64)) z x)

rewrite120.0ms (6.3%)

Memory
43.1MiB live, 43.1MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01330
01830
15829
239229
3446529
0822329
Stop Event
iter limit
node limit
iter limit
Counts
5 → 195
Calls
Call 1
Inputs
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
(*.f64 (*.f64 z y) #s(literal -4 binary64))
(*.f64 z y)
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
(*.f64 #s(literal -4 binary64) z)
Outputs
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eval37.0ms (1.9%)

Memory
25.9MiB live, 25.9MiB allocated
Compiler

Compiled 5 466 to 537 computations (90.2% saved)

prune25.0ms (1.3%)

Memory
19.9MiB live, 19.9MiB allocated
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New3190319
Fresh000
Picked022
Done000
Total3192321
Accuracy
100.0%
Counts
321 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
54.9%
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Compiler

Compiled 31 to 26 computations (16.1% saved)

regimes14.0ms (0.7%)

Memory
9.5MiB live, 9.5MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
Outputs
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
Calls

6 calls:

2.0ms
(*.f64 y #s(literal 4 binary64))
2.0ms
x
2.0ms
z
2.0ms
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
2.0ms
y
Results
AccuracySegmentsBranch
100.0%1x
100.0%1y
100.0%1z
100.0%1(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
100.0%1(*.f64 (*.f64 y #s(literal 4 binary64)) z)
100.0%1(*.f64 y #s(literal 4 binary64))
Compiler

Compiled 18 to 27 computations (-50% saved)

regimes11.0ms (0.6%)

Memory
8.8MiB live, 8.8MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Outputs
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Calls

6 calls:

2.0ms
y
2.0ms
(*.f64 y #s(literal 4 binary64))
2.0ms
z
2.0ms
x
2.0ms
(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
Results
AccuracySegmentsBranch
54.9%1x
54.9%1y
54.9%1z
54.9%1(-.f64 x (*.f64 (*.f64 y #s(literal 4 binary64)) z))
54.9%1(*.f64 (*.f64 y #s(literal 4 binary64)) z)
54.9%1(*.f64 y #s(literal 4 binary64))
Compiler

Compiled 18 to 27 computations (-50% saved)

simplify28.0ms (1.5%)

Memory
18.4MiB live, 18.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01319
11619
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
Outputs
(fma.f64 (*.f64 #s(literal -4 binary64) z) y x)
(fma.f64 (*.f64 z #s(literal -4 binary64)) y x)
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 z y) #s(literal -4 binary64)))
#s(approx (- x (* (* y 4) z)) (*.f64 (*.f64 y z) #s(literal -4 binary64)))

soundness524.0ms (27.6%)

Memory
1.9MiB live, 1.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
01015
13215
221915
3211815
0834014
038374
1105374
2262374
3894374
42564374
54474374
65491374
75869374
86083374
96195374
106237374
08299347
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 30 to 25 computations (16.7% saved)

preprocess36.0ms (1.9%)

Memory
26.5MiB live, 26.5MiB allocated
Remove

(sort y z)

Compiler

Compiled 74 to 68 computations (8.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

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