Metrics for Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C

analyze15.0ms (0.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (62.6% of total)

ival-div: 1.0ms (31.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.2s (64.6%)

Results

984.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 441.0ms

ival-mult: 227.0ms (51.5% of total)

ival-div: 198.0ms (44.9% of total)

const: 12.0ms (2.7% of total)

backward-pass: 3.0ms (0.7% of total)

Bogosity

preprocess76.0ms (4.2%)

Algorithm

2×	egg-herbie

Rules

1214×	`fnmadd-define`
1128×	`fma-define`
664×	`sum3-define`
554×	`fmsub-define`
550×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	42	30
2	104	30
3	328	30
4	1035	30
5	1992	30
6	3350	30
7	3865	30
8	3955	30
9	4123	30
10	4171	30
0	5	5
1	8	5
2	10	5
0	10	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ x (* y 2))

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

Call 2

Inputs
(/ x (* y 2))
(/ (neg x) (* y 2))
(/ x (* (neg y) 2))
(neg (/ (neg x) (* y 2)))
(neg (/ x (* (neg y) 2)))
(/ y (* x 2))

Outputs
(/ x (* y 2))
(* x (/ 1/2 y))
(/ (neg x) (* y 2))
(* x (/ -1/2 y))
(/ x (* (neg y) 2))
(* x (/ -1/2 y))
(neg (/ (neg x) (* y 2)))
(* x (/ 1/2 y))
(neg (/ x (* (neg y) 2)))
(* x (/ 1/2 y))
(/ y (* x 2))
(* y (/ 1/2 x))

Symmetry

(negabs x)

(negabs y)

explain74.0ms (4.1%)

FPErrors

Click to see full error table

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

Results

51.0ms

512×

valid

Compiler

Compiled 35 to 17 computations (51.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 4.0ms (44.1% of total)

ival-mult: 4.0ms (44.1% of total)

const: 1.0ms (11% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 x (*.f64 y #s(literal 2 binary64)))

Rules

10×	`/-lowering-/.f32`
10×	`/-lowering-/.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`
4×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	8	11
2	10	11
0	10	11

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (* y 2))
x
(* y 2)
y
2

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

localize27.0ms (1.5%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x (*.f64 y #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 y #s(literal 2 binary64))

Results

21.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (44.2% of total)

ival-mult: 2.0ms (44.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.3%)

Counts

2 → 36

Calls

Call 1

Inputs
#<alt (/ x (* y 2))>
#<alt (* y 2)>

Outputs
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>

Calls

9 calls:

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

rewrite255.0ms (14.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2730×	`/-lowering-/.f32`
2730×	`/-lowering-/.f64`
1908×	`-lowering-.f32`
1908×	`-lowering-.f64`
1146×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	16	8
2	79	8
3	397	8
4	2337	8
0	9029	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 389

Calls

Call 1

Inputs
(/ x (* y 2))
(* y 2)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (/.f64 x (/.f64 y #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 y #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 y (/.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 y (/.f64 x #s(literal 2 binary64))) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 y (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (log.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) y))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 y (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (.f64 (log.f64 (/.f64 y (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (/.f64 x (/.f64 y #s(literal 1/2 binary64))) (/.f64 y (/.f64 x #s(literal 2 binary64)))) (/.f64 x (/.f64 y #s(literal 1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 (/.f64 y #s(literal 1/2 binary64)) x) (.f64 (*.f64 y y) #s(literal 4 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) (.f64 (.f64 y y) #s(literal 4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) (.f64 x x))) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) x)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (/.f64 (/.f64 x (/.f64 y #s(literal 1/2 binary64))) (/.f64 y (/.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64))) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) x)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (/.f64 y #s(literal 1/2 binary64)) x)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 y x))) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 y x)) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -2 binary64))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 y x)) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -2 binary64))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 y x))) (.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x #s(literal 2 binary64)))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) y) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x y))) (/.f64 (*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x y))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) y)) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -2 binary64) x)) (.f64 (/.f64 y #s(literal 1/2 binary64)) y)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (/.f64 y #s(literal 1/2 binary64)) y)) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)) (.f64 (/.f64 y #s(literal 1/2 binary64)) y)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) y))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) y))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) y))) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -2 binary64) x)) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) y))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 0 binary64) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(neg.f64 (/.f64 x (/.f64 y #s(literal 1/2 binary64))))
(/.f64 x (/.f64 y #s(literal 1/2 binary64)))
(/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 y #s(literal 1/2 binary64)))))
(/.f64 (/.f64 y #s(literal 1/2 binary64)) (neg.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 y #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 y #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y (/.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 y #s(literal 1/2 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 y #s(literal 1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 y x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) y)) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y #s(literal 1/2 binary64)) y) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal -2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) y)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) y) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (/.f64 #s(literal 1/2 binary64) y)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 0 binary64) y)) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 y #s(literal 1/2 binary64)) (.f64 x x)) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 y #s(literal 1/2 binary64)) x) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -2 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) y) x) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 y (.f64 x x)) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 y x) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) (.f64 (/.f64 #s(literal -1 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (/.f64 x (/.f64 y #s(literal 1/2 binary64))) (/.f64 y (/.f64 x #s(literal 2 binary64)))) #s(literal 0 binary64)) (/.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1/2 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x (/.f64 y #s(literal 1/2 binary64)))) (/.f64 y #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 y x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 y #s(literal 1/2 binary64)) (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 y #s(literal 1/2 binary64)) y))))
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(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) y))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1/2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1/2 binary64))
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) y))
(/.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) (.f64 (.f64 y y) #s(literal 4 binary64)))
(/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (/.f64 y #s(literal 1/2 binary64)))
(/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (-.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 0 binary64)))
(/.f64 (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (/.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 (.f64 y y) #s(literal 4 binary64))))
(/.f64 (neg.f64 (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (+.f64 (/.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) #s(literal 0 binary64)) (.f64 (.f64 y y) #s(literal 4 binary64)))
(pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(*.f64 y #s(literal 2 binary64))
(*.f64 y #s(literal -2 binary64))
(*.f64 y (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) y)
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) y))
(*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 y #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 y #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 2 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) y)
(*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) y))
(.f64 (/.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y #s(literal 1/2 binary64))))
(.f64 (.f64 (*.f64 y y) #s(literal 4 binary64)) (/.f64 #s(literal 1/2 binary64) y))
(*.f64 (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) y)
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (/.f64 y #s(literal 1/2 binary64)))
(*.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) y))) (exp.f64 (log.f64 #s(literal -2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal -2 binary64))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) y))))

simplify20.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

16×	`-lowering-.f32`
16×	`-lowering-.f64`
8×	`*-commutative`
6×	`/-lowering-/.f32`
6×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	156
1	11	156
2	13	156
3	15	156
4	16	156
0	16	156

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)

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

eval43.0ms (2.4%)

Compiler: Compiled 5349 to 809 computations (84.9% saved)

prune69.0ms (3.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	425	0	425
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	425	1	426

Accuracy

100.0%

Counts

426 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness3.0ms (0.1%)

Stop Event

1×

done

Compiler

Compiled 7 to 5 computations (28.6% saved)

preprocess39.0ms (2.2%)

Remove

(negabs y)

(negabs x)

Compiler

Compiled 84 to 60 computations (28.6% saved)

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

analyze15.0ms (0.9%)

sample1.2s (64.6%)

preprocess76.0ms (4.2%)

explain74.0ms (4.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize27.0ms (1.5%)

series5.0ms (0.3%)

rewrite255.0ms (14.2%)

simplify20.0ms (1.1%)

eval43.0ms (2.4%)

prune69.0ms (3.9%)

simplify7.0ms (0.4%)

soundness3.0ms (0.1%)

preprocess39.0ms (2.2%)

end0.0ms (0%)

Profiling