Metrics for Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, G

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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)

sample625.0ms (49.9%)

Memory

-36.8MiB live, 494.7MiB allocated; 200ms collecting garbage

Samples

431.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 125.0ms

ival-add!: 79.0ms (63% of total)

ival-mult!: 45.0ms (35.9% of total)

adjust: 1.0ms (0.8% of total)

Bogosity

explain60.0ms (4.8%)

Memory

18.1MiB live, 62.8MiB allocated; 5ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`#s(literal 1 binary64)`
-	-	`(+.f64 x y)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

34.0ms

512×

valid

Compiler

Compiled 45 to 25 computations (44.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add!: 2.0ms (46.3% of total)

ival-mult!: 2.0ms (46.3% of total)

adjust: 0.0ms (0% of total)

preprocess248.0ms (19.8%)

Memory

-2.6MiB live, 185.9MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	58	34
2	179	30
3	724	30
4	1690	30
5	5931	30
0	7	5
0	11	5
1	22	5
2	36	5
3	61	5
4	142	5
5	454	5
6	4055	5
0	8118	5

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Outputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))

Symmetry

(sort x y)

Compiler

Compiled 7 to 7 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Compiler

Compiled 7 to 7 computations (0% saved)

series3.0ms (0.3%)

Memory

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

Counts

7 → 16

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x y)
x
y

Outputs
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 y)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (+ (* 1/2 x) (* 1/2 y))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx x #s(hole binary64 x))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 x)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* x (+ 1/2 (* 1/2 (/ y x))))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y x)) 1/2)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx y #s(hole binary64 y))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* y (+ 1/2 (* 1/2 (/ x y))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ x y)) 1/2)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((* (/ 1 2) (+ x y)) (/ 1 2) 1 2 (+ x y) x y)
1.0ms	y	@	inf	((* (/ 1 2) (+ x y)) (/ 1 2) 1 2 (+ x y) x y)
1.0ms	x	@	-inf	((* (/ 1 2) (+ x y)) (/ 1 2) 1 2 (+ x y) x y)
1.0ms	y	@	-inf	((* (/ 1 2) (+ x y)) (/ 1 2) 1 2 (+ x y) x y)
0.0ms	x	@	0	((* (/ 1 2) (+ x y)) (/ 1 2) 1 2 (+ x y) x y)

rewrite65.0ms (5.2%)

Memory

30.9MiB live, 76.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	183
0	63	175
1	257	175
0	1927	171

Stop Event

1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Counts

23 → 56

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x y)
x
y
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 y)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (+ (* 1/2 x) (* 1/2 y))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx x #s(hole binary64 x))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 x)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* x (+ 1/2 (* 1/2 (/ y x))))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y x)) 1/2)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx y #s(hole binary64 y))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* y (+ 1/2 (* 1/2 (/ x y))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ x y)) 1/2)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Outputs
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1/2 binary64)) (-.f64 x y))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 y (-.f64 y x) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 y (-.f64 y x) (.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 3 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (.f64 y y) #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) y)))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 y x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))) (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) y) (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (.f64 (.f64 (+.f64 y x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))
(/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 y y) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) y) (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x)))))
(fma.f64 #s(literal 1/2 binary64) y (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 y #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) y))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 y) #s(literal 1/2 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))
(-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) y) (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x))))) (/.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) y) (-.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x))))))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) y))
(+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (-.f64 y x))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 x x) (.f64 y x))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y (-.f64 y x) (.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y x) (.f64 x x))))
(+.f64 y x)
(+.f64 x y)
x
y
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 y x))
#s(approx x x)
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) x))
#s(approx (+ x y) x)
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
#s(approx (* (/ 1 2) (+ x y)) (.f64 (neg.f64 x) (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
#s(approx (+ x y) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 y x) #s(literal -1 binary64))))
#s(approx y y)
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
#s(approx (+ x y) (fma.f64 (/.f64 x y) y y))
#s(approx (* (/ 1 2) (+ x y)) (.f64 (neg.f64 y) (-.f64 (.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ x y) (*.f64 (neg.f64 y) (fma.f64 (/.f64 x y) #s(literal -1 binary64) #s(literal -1 binary64))))

eval24.0ms (2%)

Memory: -17.9MiB live, 34.0MiB allocated; 12ms collecting garbage
Compiler: Compiled 795 to 168 computations (78.9% saved)

prune2.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	3	57

Accuracy

100.0%

Counts

57 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
▶	54.0%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
▶	46.2%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 27 to 25 computations (7.4% saved)

series4.0ms (0.3%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Counts

9 → 25

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) y)
y
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)

Outputs
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 y)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (+ (* 1/2 x) (* 1/2 y))))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* 1/2 y)))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (+ (* 1/2 x) (* 1/2 y))))
#s(approx (+ y x) #s(hole binary64 y))
#s(approx (+ y x) #s(hole binary64 (+ x y)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 x)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* x (+ 1/2 (* 1/2 (/ y x))))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* x (+ 1/2 (* 1/2 (/ y x))))))
#s(approx (+ y x) #s(hole binary64 x))
#s(approx (+ y x) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y x)) 1/2)))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y x)) 1/2)))))
#s(approx (+ y x) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (* 1/2 y) #s(hole binary64 (* 1/2 y)))
#s(approx y #s(hole binary64 y))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* y (+ 1/2 (* 1/2 (/ x y))))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* y (+ 1/2 (* 1/2 (/ x y))))))
#s(approx (+ y x) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ x y)) 1/2)))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ x y)) 1/2)))))
#s(approx (+ y x) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((* (/ 1 2) (+ x y)) (* 1/2 x) 1/2 x (* (/ 1 2) (+ x y)) (* 1/2 y) y (* (+ y x) 1/2) (+ y x))
1.0ms	x	@	inf	((* (/ 1 2) (+ x y)) (* 1/2 x) 1/2 x (* (/ 1 2) (+ x y)) (* 1/2 y) y (* (+ y x) 1/2) (+ y x))
1.0ms	y	@	-inf	((* (/ 1 2) (+ x y)) (* 1/2 x) 1/2 x (* (/ 1 2) (+ x y)) (* 1/2 y) y (* (+ y x) 1/2) (+ y x))
1.0ms	y	@	inf	((* (/ 1 2) (+ x y)) (* 1/2 x) 1/2 x (* (/ 1 2) (+ x y)) (* 1/2 y) y (* (+ y x) 1/2) (+ y x))
0.0ms	x	@	0	((* (/ 1 2) (+ x y)) (* 1/2 x) 1/2 x (* (/ 1 2) (+ x y)) (* 1/2 y) y (* (+ y x) 1/2) (+ y x))

rewrite74.0ms (5.9%)

Memory

-12.3MiB live, 78.0MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	314
0	75	302
1	277	302
0	2013	296

Stop Event

1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Counts

34 → 77

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal 1/2 binary64) y)
y
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 y)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (+ (* 1/2 x) (* 1/2 y))))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* 1/2 y)))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (+ (* 1/2 x) (* 1/2 y))))
#s(approx (+ y x) #s(hole binary64 y))
#s(approx (+ y x) #s(hole binary64 (+ x y)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* 1/2 x)))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* x (+ 1/2 (* 1/2 (/ y x))))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* x (+ 1/2 (* 1/2 (/ y x))))))
#s(approx (+ y x) #s(hole binary64 x))
#s(approx (+ y x) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y x)) 1/2)))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y x)) 1/2)))))
#s(approx (+ y x) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (* 1/2 y) #s(hole binary64 (* 1/2 y)))
#s(approx y #s(hole binary64 y))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* y (+ 1/2 (* 1/2 (/ x y))))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* y (+ 1/2 (* 1/2 (/ x y))))))
#s(approx (+ y x) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (* (/ 1 2) (+ x y)) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ x y)) 1/2)))))
#s(approx (* (+ y x) 1/2) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ x y)) 1/2)))))
#s(approx (+ y x) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Outputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) y)
y
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 y x))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1/2 binary64)) (-.f64 x y))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1/2 binary64)) (-.f64 y x))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 y (-.f64 y x) (.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (-.f64 y x) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 x (-.f64 x y) (.f64 y y)))
(/.f64 (-.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 3 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (fma.f64 (.f64 y y) #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal -1/2 binary64) y)))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 y x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))) (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 y #s(literal 1/2 binary64)) (-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (.f64 (+.f64 y x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 y y) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (*.f64 x #s(literal 1/2 binary64)) y) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 y #s(literal 1/2 binary64)) (-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))))))
(fma.f64 y #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) y (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 y #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (neg.f64 y) #s(literal 1/2 binary64)))
(-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) y))
(-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) x))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 y #s(literal 1/2 binary64)) (-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))))) (/.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 y #s(literal 1/2 binary64)) (-.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(+.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (-.f64 y x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y (-.f64 y x) (.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y (-.f64 y x) (.f64 x x))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))))
(+.f64 y x)
(+.f64 x y)
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
#s(approx (* 1/2 x) (*.f64 x #s(literal 1/2 binary64)))
#s(approx x x)
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
#s(approx (+ y x) y)
#s(approx (+ y x) (+.f64 y x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) x))
#s(approx (+ y x) x)
#s(approx (+ y x) (fma.f64 (/.f64 y x) x x))
#s(approx (* (/ 1 2) (+ x y)) (.f64 (neg.f64 x) (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 2) (+ x y)) (.f64 (neg.f64 x) (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 1/2 binary64))))
#s(approx (+ y x) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 y x) #s(literal -1 binary64))))
#s(approx (* 1/2 y) (*.f64 y #s(literal 1/2 binary64)))
#s(approx y y)
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) y))
#s(approx (+ y x) (fma.f64 (/.f64 x y) y y))
#s(approx (* (/ 1 2) (+ x y)) (.f64 (neg.f64 y) (-.f64 (.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (/ 1 2) (+ x y)) (.f64 (neg.f64 y) (-.f64 (.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ y x) (*.f64 (neg.f64 y) (fma.f64 (/.f64 x y) #s(literal -1 binary64) #s(literal -1 binary64))))

eval7.0ms (0.6%)

Memory: 15.3MiB live, 15.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 022 to 198 computations (80.6% saved)

prune17.0ms (1.4%)

Memory

-36.9MiB live, 9.2MiB allocated; 3ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	74	3	77

Accuracy

100.0%

Counts

77 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
✓	54.0%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
✓	46.2%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 61 to 44 computations (27.9% saved)

regimes8.0ms (0.6%)

Memory

19.9MiB live, 19.9MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Outputs
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))

Calls

4 calls:

2.0ms	y
2.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
2.0ms	x
2.0ms	(+.f64 x y)

Results

Accuracy	Segments	Branch
100.0%	1	`(+.f64 x y)`
100.0%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes6.0ms (0.4%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))

Outputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y))

Calls

4 calls:

1.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
1.0ms	y
1.0ms	(+.f64 x y)
1.0ms	x

Results

Accuracy	Segments	Branch
96.7%	2	`(+.f64 x y)`
96.7%	2	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
78.7%	2	`x`
85.1%	2	`y`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes22.0ms (1.7%)

Memory

-36.4MiB live, 14.9MiB allocated; 33ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Outputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Calls

4 calls:

16.0ms	y
3.0ms	x
1.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
1.0ms	(+.f64 x y)

Results

Accuracy	Segments	Branch
46.2%	1	`x`
46.2%	1	`y`
46.2%	1	`(+.f64 x y)`
46.2%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.7050552080741447e-267	5.535898116098229e-258

Compiler

Compiled 10 to 12 computations (-20% saved)

simplify42.0ms (3.3%)

Memory

6.5MiB live, 50.7MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	33	42
2	62	42
3	237	42
4	1199	42
5	4907	42

Stop Event

1×	node limit

Calls

Call 1

Inputs

(*.f64 (+.f64 y x) #s(literal 1/2 binary64))

(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) #s(literal -290432989937067/290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224570063240272065048916911180770489396052896597871561450348236492274894506629430939420761276732468592926240515079310107169312085954718183386786847281838290059659012482973391669690368 binary64)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y)))

#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

Outputs

(*.f64 (+.f64 y x) #s(literal 1/2 binary64))

(if (<=.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) #s(literal -290432989937067/290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224570063240272065048916911180770489396052896597871561450348236492274894506629430939420761276732468592926240515079310107169312085954718183386786847281838290059659012482973391669690368 binary64)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y)))

#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

derivations16.0ms (1.3%)

Memory

29.6MiB live, 29.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 48 to 22 computations (54.2% saved)

preprocess28.0ms (2.2%)

Memory: -24.4MiB live, 66.2MiB allocated; 9ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 216 to 138 computations (36.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample625.0ms (49.9%)

explain60.0ms (4.8%)

preprocess248.0ms (19.8%)

eval0.0ms (0%)

prune0.0ms (0%)

series3.0ms (0.3%)

rewrite65.0ms (5.2%)

eval24.0ms (2%)

prune2.0ms (0.2%)

series4.0ms (0.3%)

rewrite74.0ms (5.9%)

eval7.0ms (0.6%)

prune17.0ms (1.4%)

regimes8.0ms (0.6%)

regimes6.0ms (0.4%)

regimes22.0ms (1.7%)

bsearch0.0ms (0%)

simplify42.0ms (3.3%)

derivations16.0ms (1.3%)

preprocess28.0ms (2.2%)

end0.0ms (0%)

Profiling