Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Time bar (total: 2.8s)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
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 11 to 11 computations (0% saved)

sample1.2s (41.1%)

Memory
9.3MiB live, 1 536.1MiB allocated; 442ms collecting garbage
Samples
680.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 410.0ms
ival-div: 165.0ms (40.3% of total)
ival-mult: 137.0ms (33.4% of total)
ival-sub: 87.0ms (21.2% of total)
exact: 10.0ms (2.4% of total)
ival-true: 6.0ms (1.5% of total)
adjust: 3.0ms (0.7% of total)
ival-assert: 3.0ms (0.7% of total)
Bogosity

explain104.0ms (3.7%)

Memory
22.8MiB live, 160.3MiB allocated; 13ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-#s(literal 8 binary64)
00-0-(/.f64 (*.f64 x y) #s(literal 2 binary64))
00-0-z
00-0-(*.f64 x y)
00-0-(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
00-0-(/.f64 z #s(literal 8 binary64))
00-0-#s(literal 2 binary64)
00-0-y
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
52.0ms512×0valid
Compiler

Compiled 63 to 31 computations (50.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-mult: 23.0ms (69.9% of total)
ival-div: 6.0ms (18.2% of total)
ival-sub: 2.0ms (6.1% of total)
exact: 1.0ms (3% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess244.0ms (8.7%)

Memory
25.1MiB live, 159.9MiB allocated; 29ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03390
15288
27184
311184
417784
536784
6172584
7587884
099
0139
1189
2249
3379
4659
51689
610479
755219
084259
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
Outputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
Symmetry

(sort x y)

Compiler

Compiled 9 to 9 computations (0% saved)

eval0.0ms (0%)

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

Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
Compiler

Compiled 9 to 9 computations (0% saved)

series12.0ms (0.4%)

Memory
-27.2MiB live, 17.8MiB allocated; 6ms collecting garbage
Counts
9 → 15
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
x
y
#s(literal 2 binary64)
(/.f64 z #s(literal 8 binary64))
z
#s(literal 8 binary64)
Outputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
x
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/8 z)
z
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8)
1.0ms
y
@inf
((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8)
1.0ms
x
@0
((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8)
1.0ms
y
@-inf
((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8)
1.0ms
y
@0
((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8)

simplify222.0ms (7.9%)

Memory
35.5MiB live, 273.6MiB allocated; 72ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04289
112889
244489
3111789
4331189
5655889
0859081
Stop Event
iter limit
node limit
Counts
15 → 12
Calls
Call 1
Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
x
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/8 z)
z
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* 1/2 (* x y))
(*.f64 (*.f64 y x) #s(literal 1/2 binary64))
(* x y)
(*.f64 y x)
x
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* 1/8 z)
(*.f64 #s(literal 1/8 binary64) z)
z
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))

rewrite92.0ms (3.3%)

Memory
-29.6MiB live, 109.1MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0925
01325
14525
031925
Stop Event
iter limit
iter limit
iter limit
unsound
iter limit
Counts
9 → 34
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(*.f64 x y)
x
y
#s(literal 2 binary64)
(/.f64 z #s(literal 8 binary64))
z
#s(literal 8 binary64)
Outputs
(/.f64 (/.f64 (fma.f64 #s(literal 8 binary64) (*.f64 y x) (*.f64 #s(literal -2 binary64) z)) #s(literal 2 binary64)) #s(literal 8 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (*.f64 y x) (*.f64 #s(literal -2 binary64) z))) #s(literal -16 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) y) #s(literal -8 binary64)) (*.f64 #s(literal -2 binary64) (neg.f64 z))) #s(literal 16 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) y) #s(literal 8 binary64)) (*.f64 #s(literal -2 binary64) z)) #s(literal -16 binary64))
(/.f64 (-.f64 (*.f64 (*.f64 y x) #s(literal -8 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 z))) #s(literal -16 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 8 binary64) (*.f64 y x) (*.f64 #s(literal -2 binary64) z)) #s(literal 16 binary64))
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64)))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 8 binary64) (*.f64 y x)) #s(literal 16 binary64)) (/.f64 (*.f64 z #s(literal 2 binary64)) #s(literal 16 binary64)))
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(*.f64 (/.f64 y #s(literal 2 binary64)) x)
(*.f64 y (/.f64 x #s(literal 2 binary64)))
(*.f64 x (/.f64 y #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) y)) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 x) y) #s(literal -2 binary64))
(/.f64 (*.f64 y x) #s(literal 2 binary64))
(neg.f64 (/.f64 (*.f64 (neg.f64 x) y) #s(literal 2 binary64)))
(neg.f64 (/.f64 (*.f64 y x) #s(literal -2 binary64)))
(*.f64 y x)
(*.f64 x y)
x
y
#s(literal 2 binary64)
(/.f64 (neg.f64 (neg.f64 z)) #s(literal 8 binary64))
(/.f64 (neg.f64 z) #s(literal -8 binary64))
(/.f64 z #s(literal 8 binary64))
(neg.f64 (/.f64 (neg.f64 z) #s(literal 8 binary64)))
(neg.f64 (/.f64 z #s(literal -8 binary64)))
z
#s(literal 8 binary64)

eval4.0ms (0.1%)

Memory
15.0MiB live, 15.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 554 to 118 computations (78.7% saved)

prune2.0ms (0.1%)

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New37239
Fresh000
Picked101
Done000
Total38240
Accuracy
100.0%
Counts
40 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
46.8%
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
Compiler

Compiled 31 to 27 computations (12.9% saved)

series12.0ms (0.4%)

Memory
-27.3MiB live, 28.9MiB allocated; 6ms collecting garbage
Counts
10 → 14
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
Outputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 x)
x
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
z
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
Calls

9 calls:

TimeVariablePointExpression
7.0ms
z
@inf
((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y)
1.0ms
x
@-inf
((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y)
1.0ms
z
@-inf
((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y)
1.0ms
x
@inf
((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y)
1.0ms
x
@0
((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y)

simplify257.0ms (9.2%)

Memory
39.5MiB live, 313.9MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04286
112886
244586
3111986
4333986
5660586
0863478
Stop Event
iter limit
node limit
Counts
14 → 11
Calls
Call 1
Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 x)
x
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
z
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(* 1/2 (* x y))
(*.f64 #s(literal 1/2 binary64) (*.f64 y x))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
z
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))

rewrite38.0ms (1.4%)

Memory
-2.9MiB live, 44.5MiB allocated; 1ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01650
02050
17350
053350
Stop Event
iter limit
iter limit
node limit
iter limit
Counts
10 → 36
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
#s(literal -1/8 binary64)
z
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
(*.f64 #s(literal -1/8 binary64) z)
(*.f64 z #s(literal -1/8 binary64))
#s(literal -1/8 binary64)
z
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/8 binary64) z) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 z z) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal 1/8 binary64) z)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 z #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z)))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 z #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64))) (fma.f64 #s(literal 1/64 binary64) (*.f64 z z) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal -1/8 binary64)) z))))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 z #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal -1/8 binary64) z))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/8 binary64) z))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z))
(fma.f64 #s(literal -1/8 binary64) z (*.f64 (*.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 z #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) z))
(fma.f64 y (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/8 binary64) z))
(fma.f64 x (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal -1/8 binary64) z))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z))) (/.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z))))
(-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 (neg.f64 z) #s(literal -1/8 binary64)))
(-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal 1/8 binary64) z))
(-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) y))
(-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 #s(literal -1/2 binary64) (*.f64 y x)))
(-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (neg.f64 y) (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))))
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal -1/8 binary64) z))
(+.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
y

eval4.0ms (0.2%)

Memory
12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 010 to 131 computations (87% saved)

prune25.0ms (0.9%)

Memory
-45.8MiB live, 12.3MiB allocated; 4ms collecting garbage
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New43144
Fresh000
Picked022
Done000
Total43346
Accuracy
100.0%
Counts
46 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
54.7%
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
46.8%
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
Compiler

Compiled 46 to 40 computations (13% saved)

series4.0ms (0.2%)

Memory
10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Counts
6 → 13
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y x))
#s(literal 1/2 binary64)
(*.f64 y x)
y
x
Outputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
x
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x)
1.0ms
y
@-inf
((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x)
1.0ms
x
@inf
((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x)
1.0ms
y
@inf
((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x)
0.0ms
x
@0
((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x)

simplify236.0ms (8.4%)

Memory
23.5MiB live, 218.9MiB allocated; 20ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04285
112885
244485
3111585
4332085
5655685
0858777
Stop Event
iter limit
node limit
Counts
13 → 11
Calls
Call 1
Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x y)
x
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* 1/2 (* x y))
(*.f64 #s(literal 1/2 binary64) (*.f64 y x))
(* x y)
(*.f64 y x)
x
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
y
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(+ (* -1/8 z) (* 1/2 (* x y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))

rewrite95.0ms (3.4%)

Memory
-26.3MiB live, 65.4MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01326
01526
15126
033226
Stop Event
iter limit
iter limit
iter limit
unsound
iter limit
Counts
6 → 12
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 y x))
#s(literal 1/2 binary64)
(*.f64 y x)
y
x
Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 (*.f64 #s(literal 1/2 binary64) y) x)
(*.f64 #s(literal 1/2 binary64) (*.f64 y x))
(*.f64 (*.f64 y x) #s(literal 1/2 binary64))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x (*.f64 #s(literal 1/2 binary64) y))
#s(literal 1/2 binary64)
(*.f64 y x)
(*.f64 x y)
y
x

eval2.0ms (0.1%)

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

Compiled 251 to 42 computations (83.3% saved)

prune4.0ms (0.1%)

Memory
9.8MiB live, 9.8MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New16016
Fresh000
Picked011
Done022
Total16319
Accuracy
100.0%
Counts
19 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
54.7%
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
46.8%
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
Compiler

Compiled 101 to 65 computations (35.6% saved)

regimes16.0ms (0.6%)

Memory
-6.3MiB live, 38.3MiB allocated; 5ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
Calls

7 calls:

5.0ms
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
2.0ms
z
2.0ms
(/.f64 z #s(literal 8 binary64))
2.0ms
x
2.0ms
y
Results
AccuracySegmentsBranch
100.0%1(/.f64 z #s(literal 8 binary64))
100.0%1(*.f64 x y)
100.0%1(/.f64 (*.f64 x y) #s(literal 2 binary64))
100.0%1(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
100.0%1x
100.0%1y
100.0%1z
Compiler

Compiled 23 to 33 computations (-43.5% saved)

regimes16.0ms (0.6%)

Memory
-19.6MiB live, 29.3MiB allocated; 9ms collecting garbage
Counts
2 → 3
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))
Calls

7 calls:

8.0ms
(/.f64 z #s(literal 8 binary64))
1.0ms
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
1.0ms
z
1.0ms
x
1.0ms
y
Results
AccuracySegmentsBranch
71.6%3(/.f64 z #s(literal 8 binary64))
82.7%3(*.f64 x y)
82.7%3(/.f64 (*.f64 x y) #s(literal 2 binary64))
73.2%7(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
80.1%3x
75.6%3y
71.6%3z
Compiler

Compiled 23 to 33 computations (-43.5% saved)

regimes8.0ms (0.3%)

Memory
23.4MiB live, 23.4MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
Calls

7 calls:

1.0ms
(/.f64 z #s(literal 8 binary64))
1.0ms
(/.f64 (*.f64 x y) #s(literal 2 binary64))
1.0ms
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
1.0ms
z
1.0ms
x
Results
AccuracySegmentsBranch
46.8%1(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
46.8%1(/.f64 z #s(literal 8 binary64))
46.8%1z
46.8%1y
46.8%1x
46.8%1(*.f64 x y)
46.8%1(/.f64 (*.f64 x y) #s(literal 2 binary64))
Compiler

Compiled 23 to 33 computations (-43.5% saved)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated; 0ms collecting garbage
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
1.935661504659047e-25
3.1924317173137033e-25
0.0ms
-1.4459489187182815e-55
-3.481194635533033e-57
Compiler

Compiled 12 to 15 computations (-25% saved)

simplify41.0ms (1.5%)

Memory
-8.6MiB live, 36.6MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02776
13576
24176
35576
49576
543376
6363976
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -5521397077432451/55213970774324510299478046898216203619608871777363092441300193790394368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) (if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 8711228593176025/43556142965880123323311949751266331066368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))
Outputs
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)))
(if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -5521397077432451/55213970774324510299478046898216203619608871777363092441300193790394368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) (if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 8711228593176025/43556142965880123323311949751266331066368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))))
(if (or (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -5521397077432451/55213970774324510299478046898216203619608871777363092441300193790394368 binary64)) (not (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 8711228593176025/43556142965880123323311949751266331066368 binary64)))) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)))
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))

derivations197.0ms (7%)

Memory
-6.8MiB live, 136.0MiB allocated; 12ms collecting garbage
Stop Event
done
Compiler

Compiled 76 to 29 computations (61.8% saved)

preprocess20.0ms (0.7%)

Memory
1.1MiB live, 46.9MiB allocated; 4ms collecting garbage
Remove

(sort x y)

Compiler

Compiled 206 to 106 computations (48.5% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...