Metrics for Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, E

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

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 7 to 7 computations (0% saved)

sample699.0ms (29.5%)

Memory

-98.6MiB live, 840.4MiB allocated

Samples

515.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 354.0ms

ival-div: 300.0ms (84.8% of total)

ival-sub: 40.0ms (11.3% of total)

ival-true: 6.0ms (1.7% of total)

exact: 5.0ms (1.4% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain48.0ms (2%)

Memory

18.6MiB live, 97.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 x (/.f64 y #s(literal 4 binary64)))`
-	-	`y`
-	-	`(/.f64 y #s(literal 4 binary64))`
-	-	`#s(literal 4 binary64)`
-	-	`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

19.0ms

512×

valid

Compiler

Compiled 33 to 19 computations (42.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (52.2% of total)

ival-sub: 2.0ms (26.1% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess33.0ms (1.4%)

Memory

-12.2MiB live, 68.1MiB allocated

Algorithm

1×	egg-herbie

Rules

128×	`lower-fma.f64`
128×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
46×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	30	27
2	74	25
3	152	25
4	250	25
5	293	25
6	299	25
0	5	5
0	7	5
1	9	5
2	19	5
3	27	5
4	39	5
5	58	5
6	94	5
7	126	5
8	182	5
9	213	5
10	246	5
11	247	5
0	247	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 y #s(literal 4 binary64)))

Outputs
(-.f64 x (/.f64 y #s(literal 4 binary64)))
(fma.f64 y #s(literal -1/4 binary64) x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.8MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (/.f64 y #s(literal 4 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify10.0ms (0.4%)

Memory

20.5MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	128	(-.f64 x (/.f64 y #s(literal 4 binary64)))
cost-diff	384	(/.f64 y #s(literal 4 binary64))

Rules

128×	`lower-fma.f64`
128×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
40×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	7	11
1	9	11
2	19	11
3	27	11
4	39	11
5	58	11
6	94	11
7	126	11
8	182	11
9	213	11
10	246	11
11	247	11
0	247	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 x (/.f64 y #s(literal 4 binary64)))
x
(/.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)

Outputs
(-.f64 x (/.f64 y #s(literal 4 binary64)))
(fma.f64 y #s(literal -1/4 binary64) x)
x
(/.f64 y #s(literal 4 binary64))
(*.f64 y #s(literal 1/4 binary64))
y
#s(literal 4 binary64)

localize16.0ms (0.7%)

Memory

-1.4MiB live, 37.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 y #s(literal 4 binary64))
accuracy	0	(-.f64 x (/.f64 y #s(literal 4 binary64)))

Samples

11.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-div: 2.0ms (59.5% of total)

ival-sub: 1.0ms (29.8% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs
#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())

Inputs

#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())

#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/4 y) (taylor 0 y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor 0 y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor 0 y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor 0 y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor -inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor -inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor -inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 y) (taylor -inf y) (#s(alt (/.f64 y #s(literal 4 binary64)) (patch (/.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 1/4 y)) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 1/4 y)) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 1/4 y)) (taylor 0 x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x (/.f64 y #s(literal 4 binary64))) (patch (-.f64 x (/.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(- x (/ y 4))
0.0ms	y	@	-inf	(/ y 4)
0.0ms	y	@	inf	(/ y 4)
0.0ms	y	@	0	(/ y 4)
0.0ms	x	@	inf	(- x (/ y 4))

simplify227.0ms (9.6%)

Memory

7.1MiB live, 240.9MiB allocated

Algorithm

1×	egg-herbie

Rules

3 160×	`lower-fma.f64`
3 160×	`lower-fma.f32`
2 584×	`lower-*.f64`
2 584×	`lower-*.f32`
2 384×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	138
1	68	138
2	170	138
3	455	138
4	1251	138
5	2440	138
6	3244	138
7	3580	138
8	3876	138
9	4060	138
10	5213	138
11	6009	138
12	6777	138
13	7045	138
14	7825	138
0	8361	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 33

Calls

Call 1

Inputs
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* -1/4 y)
(- x (* 1/4 y))
(- x (* 1/4 y))
(- x (* 1/4 y))
x
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
x
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(* -1/4 y)
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* -1/4 y)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))

Outputs
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* 1/4 y)
(*.f64 #s(literal 1/4 binary64) y)
(* -1/4 y)
(*.f64 y #s(literal -1/4 binary64))
(- x (* 1/4 y))
(fma.f64 y #s(literal -1/4 binary64) x)
(- x (* 1/4 y))
(fma.f64 y #s(literal -1/4 binary64) x)
(- x (* 1/4 y))
(fma.f64 y #s(literal -1/4 binary64) x)
x
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 y #s(literal -1/4 binary64) x)
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 y #s(literal -1/4 binary64) x)
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 y #s(literal -1/4 binary64) x)
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 y #s(literal -1/4 binary64) x)
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 y #s(literal -1/4 binary64) x)
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 y #s(literal -1/4 binary64) x)
x
(+ x (* -1/4 y))
(fma.f64 y #s(literal -1/4 binary64) x)
(+ x (* -1/4 y))
(fma.f64 y #s(literal -1/4 binary64) x)
(+ x (* -1/4 y))
(fma.f64 y #s(literal -1/4 binary64) x)
(* -1/4 y)
(*.f64 y #s(literal -1/4 binary64))
(* y (- (/ x y) 1/4))
(fma.f64 y #s(literal -1/4 binary64) x)
(* y (- (/ x y) 1/4))
(fma.f64 y #s(literal -1/4 binary64) x)
(* y (- (/ x y) 1/4))
(fma.f64 y #s(literal -1/4 binary64) x)
(* -1/4 y)
(*.f64 y #s(literal -1/4 binary64))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 y #s(literal -1/4 binary64) x)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 y #s(literal -1/4 binary64) x)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 y #s(literal -1/4 binary64) x)

rewrite189.0ms (8%)

Memory

-17.5MiB live, 258.0MiB allocated

Rules

3 368×	`lower-fma.f64`
3 368×	`lower-fma.f32`
3 224×	`lower-*.f64`
3 224×	`lower-*.f32`
2 912×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
0	7	8
1	32	8
2	248	8
3	4066	8
0	8150	7

Stop Event

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

Counts

2 → 130

Calls

Call 1

Inputs
(/.f64 y #s(literal 4 binary64))
(-.f64 x (/.f64 y #s(literal 4 binary64)))

Outputs
(exp.f64 (log.f64 (*.f64 y #s(literal 1/4 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 y #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 y #s(literal -1/4 binary64)))
(neg.f64 (*.f64 y #s(literal -1/4 binary64)))
(neg.f64 (.f64 (.f64 y #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(/.f64 y #s(literal 4 binary64))
(/.f64 (neg.f64 y) #s(literal -4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) y))
(/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) y))
(/.f64 (exp.f64 (log.f64 (neg.f64 y))) (exp.f64 (log.f64 #s(literal -4 binary64))))
(/.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 #s(literal 4 binary64))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (neg.f64 (log.f64 (*.f64 y #s(literal -1/4 binary64))))))
(pow.f64 (*.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 16 binary64) (*.f64 y y)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 y #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (*.f64 y #s(literal 1/4 binary64)))))
(*.f64 y #s(literal 1/4 binary64))
(.f64 (.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))
(*.f64 (neg.f64 y) #s(literal -1/4 binary64))
(.f64 #s(literal 1 binary64) (.f64 y #s(literal 1/4 binary64)))
(*.f64 #s(literal 1/4 binary64) y)
(*.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 1 binary64)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 y #s(literal -1/4 binary64)))
(.f64 #s(literal -1 binary64) (pow.f64 (.f64 y #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/4 binary64) (neg.f64 y))
(*.f64 #s(literal -1/4 binary64) (pow.f64 (neg.f64 y) #s(literal 1 binary64)))
(*.f64 #s(literal -1/4 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 y)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) #s(literal 1/4 binary64))
(.f64 (pow.f64 (.f64 y #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 y #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 y) #s(literal 1 binary64)) #s(literal -1/4 binary64))
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(/.f64 (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (.f64 y (.f64 y y)) (.f64 #s(literal 1/4096 binary64) (.f64 y (.f64 y y))))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 (.f64 y (.f64 #s(literal 1/16 binary64) y)) (fma.f64 y (.f64 #s(literal 1/16 binary64) y) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 y (.f64 #s(literal 1/16 binary64) y) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 y (.f64 #s(literal 1/16 binary64) y) (.f64 x x)))
(/.f64 (-.f64 (neg.f64 (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (neg.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (*.f64 x x))))
(/.f64 (-.f64 (neg.f64 (.f64 x x)) (.f64 (*.f64 y y) #s(literal -1/16 binary64))) (fma.f64 y #s(literal -1/4 binary64) (neg.f64 x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x)) (.f64 (fma.f64 y #s(literal -1/4 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x)))))
(.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x)) (/.f64 (fma.f64 y #s(literal -1/4 binary64) x) (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (*.f64 x x))))
(*.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x))
(.f64 (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)))
(.f64 (fma.f64 y #s(literal 1/4 binary64) x) (.f64 (fma.f64 y #s(literal -1/4 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))))
(*.f64 (fma.f64 y #s(literal 1/4 binary64) x) (/.f64 (fma.f64 y #s(literal -1/4 binary64) x) (fma.f64 y #s(literal 1/4 binary64) x)))
(.f64 (neg.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (*.f64 x x)))))
(.f64 (neg.f64 (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) (neg.f64 x))))
(.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x))) (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (*.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (.f64 x x)) (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (.f64 x x)))) (fma.f64 (.f64 y #s(literal 1/4 binary64)) (-.f64 (.f64 y #s(literal 1/4 binary64)) x) (.f64 x x)))
(.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (*.f64 x x))) (fma.f64 y #s(literal -1/4 binary64) x))
(.f64 (/.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (.f64 x x))) (fma.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) (.f64 (fma.f64 y #s(literal 1/4 binary64) x) (.f64 (fma.f64 y #s(literal 1/4 binary64) x) (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (-.f64 (.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (.f64 x x))) (.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x)) (fma.f64 x x (.f64 (.f64 y #s(literal -1/4 binary64)) (fma.f64 y #s(literal 1/4 binary64) x))))) (fma.f64 x x (.f64 (.f64 y #s(literal -1/4 binary64)) (fma.f64 y #s(literal 1/4 binary64) x))))
(.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 1/262144 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)) (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x x)) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (.f64 y (.f64 y y)) (.f64 #s(literal 1/4096 binary64) (.f64 y (.f64 y y)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64) (.f64 x (*.f64 x x)))))
(.f64 (pow.f64 (/.f64 (fma.f64 y #s(literal 1/4 binary64) x) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (.f64 y (.f64 y y)) (.f64 #s(literal 1/4096 binary64) (.f64 y (.f64 y y)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y (.f64 #s(literal 1/16 binary64) y)) (fma.f64 y (.f64 #s(literal 1/16 binary64) y) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 y #s(literal 1/4 binary64) x) (.f64 (fma.f64 y (.f64 #s(literal 1/16 binary64) y) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 #s(literal 1/16 binary64) y) (.f64 x x))))

eval50.0ms (2.1%)

Memory: -5.0MiB live, 31.0MiB allocated
Compiler: Compiled 3 392 to 380 computations (88.8% saved)

prune19.0ms (0.8%)

Memory

31.2MiB live, 31.2MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	2	164

Accuracy

100.0%

Counts

164 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 y #s(literal -1/4 binary64) x)
▶	48.8%	#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify15.0ms (0.6%)

Memory

-41.9MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 y #s(literal -1/4 binary64) x)
cost-diff	0	(*.f64 y #s(literal -1/4 binary64))
cost-diff	0	#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Rules

128×	`lower-fma.f32`
126×	`lower-fma.f64`
80×	`lower-*.f32`
78×	`lower-*.f64`
40×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	21
0	11	22
1	15	22
2	25	22
3	33	22
4	46	20
5	70	20
6	105	20
7	134	20
8	191	20
9	222	20
10	255	20
11	256	20
0	256	20

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))
(*.f64 y #s(literal -1/4 binary64))
y
#s(literal -1/4 binary64)
(fma.f64 y #s(literal -1/4 binary64) x)
y
#s(literal -1/4 binary64)
x

Outputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))
(*.f64 y #s(literal -1/4 binary64))
y
#s(literal -1/4 binary64)
(fma.f64 y #s(literal -1/4 binary64) x)
y
#s(literal -1/4 binary64)
x

localize24.0ms (1%)

Memory

2.6MiB live, 39.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y #s(literal -1/4 binary64) x)
accuracy	0	(*.f64 y #s(literal -1/4 binary64))
accuracy	32.79362188370393	#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Samples

13.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (31.6% of total)

ival-mult: 2.0ms (31.6% of total)

ival-sub: 1.0ms (15.8% of total)

ival-add: 1.0ms (15.8% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs

#s(alt #s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())

#s(alt (*.f64 y #s(literal -1/4 binary64)) (patch (*.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())

#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt (* -1/4 y) (taylor 0 x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 1/4 y)) (taylor 0 x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 1/4 y)) (taylor 0 x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (- x (* 1/4 y)) (taylor 0 x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) (patch #s(approx (- x (/ y 4)) (.f64 y #s(literal -1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal -1/4 binary64)) (patch (.f64 y #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1/4)) (taylor inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor -inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1/4 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/4 y) (taylor 0 x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/4 y)) (taylor 0 x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/4 (/ y x)))) (taylor inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/4 (/ y x)) 1))) (taylor -inf x) (#s(alt (fma.f64 y #s(literal -1/4 binary64) x) (patch (fma.f64 y #s(literal -1/4 binary64) x) #<representation binary64>) () ())) ())

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(* y -1/4)
0.0ms	x	@	0	(+ (* y -1/4) x)
0.0ms	x	@	-inf	(+ (* y -1/4) x)
0.0ms	x	@	inf	(+ (* y -1/4) x)
0.0ms	x	@	-inf	(- x (/ y 4))

simplify260.0ms (11%)

Memory

14.5MiB live, 213.0MiB allocated

Algorithm

1×	egg-herbie

Rules

3 160×	`lower-fma.f64`
3 160×	`lower-fma.f32`
2 584×	`lower-*.f64`
2 584×	`lower-*.f32`
2 384×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	240
1	68	240
2	170	240
3	455	240
4	1250	240
5	2461	240
6	3264	240
7	3600	240
8	3896	240
9	4079	240
10	5224	240
11	6020	240
12	6788	240
13	7056	240
14	7836	240
0	8372	204

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

Inputs
(* -1/4 y)
(- x (* 1/4 y))
(- x (* 1/4 y))
(- x (* 1/4 y))
x
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
x
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(* -1/4 y)
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* -1/4 y)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
(* -1/4 y)
x
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(* -1/4 y)
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* -1/4 y)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(* -1/4 y)
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(+ x (* -1/4 y))
x
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
(* x (+ 1 (* -1/4 (/ y x))))
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(* -1 (* x (- (* 1/4 (/ y x)) 1)))

Outputs
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(- x (* 1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(- x (* 1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(- x (* 1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
x
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 #s(literal -1/4 binary64) y x)
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 #s(literal -1/4 binary64) y x)
x
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* y (- (/ x y) 1/4))
(fma.f64 #s(literal -1/4 binary64) y x)
(* y (- (/ x y) 1/4))
(fma.f64 #s(literal -1/4 binary64) y x)
(* y (- (/ x y) 1/4))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
x
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* y (- (/ x y) 1/4))
(fma.f64 #s(literal -1/4 binary64) y x)
(* y (- (/ x y) 1/4))
(fma.f64 #s(literal -1/4 binary64) y x)
(* y (- (/ x y) 1/4))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* y (+ 1/4 (* -1 (/ x y)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1/4 y)
(*.f64 #s(literal -1/4 binary64) y)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
(+ x (* -1/4 y))
(fma.f64 #s(literal -1/4 binary64) y x)
x
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 #s(literal -1/4 binary64) y x)
(* x (+ 1 (* -1/4 (/ y x))))
(fma.f64 #s(literal -1/4 binary64) y x)
x
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 #s(literal -1/4 binary64) y x)
(* -1 (* x (- (* 1/4 (/ y x)) 1)))
(fma.f64 #s(literal -1/4 binary64) y x)

rewrite200.0ms (8.5%)

Memory

-5.9MiB live, 311.8MiB allocated

Rules

4 868×	`lower-fma.f32`
4 866×	`lower-fma.f64`
3 436×	`lower-*.f32`
3 434×	`lower-*.f64`
2 340×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
0	11	17
1	48	15
2	398	15
3	6483	15
0	8207	15

Stop Event

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

Counts

3 → 141

Calls

Call 1

Inputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))
(*.f64 y #s(literal -1/4 binary64))
(fma.f64 y #s(literal -1/4 binary64) x)

Outputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 y #s(literal -1/4 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 y #s(literal -1/4 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 y #s(literal -1/4 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 y #s(literal 1/4 binary64)))
(neg.f64 (*.f64 y #s(literal 1/4 binary64)))
(/.f64 y #s(literal -4 binary64))
(/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 #s(literal 0 binary64) (.f64 y #s(literal 1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -4 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 4 binary64) y))
(/.f64 (neg.f64 y) #s(literal 4 binary64))
(/.f64 (.f64 (.f64 y y) #s(literal -1/16 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 y #s(literal 1/4 binary64))))
(pow.f64 (*.f64 y #s(literal -1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -4 binary64) y) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -4 binary64) y) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 y #s(literal -1/4 binary64))
(.f64 (.f64 y #s(literal 1/4 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal -1/4 binary64) y)
(.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/4 binary64)))
(*.f64 #s(literal 1/4 binary64) (neg.f64 y))
(.f64 #s(literal -1 binary64) (.f64 y #s(literal 1/4 binary64)))
(*.f64 (neg.f64 y) #s(literal 1/4 binary64))
(+.f64 x (*.f64 y #s(literal -1/4 binary64)))
(+.f64 (*.f64 y #s(literal -1/4 binary64)) x)
(+.f64 (/.f64 (.f64 (.f64 y y) #s(literal -1/16 binary64)) (fma.f64 y #s(literal 1/4 binary64) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -1/4 binary64)) x))))
(+.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))) (neg.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (*.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))))
(+.f64 (/.f64 (.f64 x x) (fma.f64 y #s(literal 1/4 binary64) x)) (neg.f64 (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x))) #s(literal -1 binary64)))
(-.f64 x (*.f64 y #s(literal 1/4 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 y #s(literal 1/4 binary64)) x))
(-.f64 (/.f64 (.f64 (.f64 y y) #s(literal -1/16 binary64)) (fma.f64 y #s(literal 1/4 binary64) x)) (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -1/4 binary64)) x)))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))) (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (*.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))))
(-.f64 (/.f64 (.f64 x x) (fma.f64 y #s(literal 1/4 binary64) x)) (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x)))
(-.f64 (+.f64 x #s(literal 0 binary64)) (*.f64 y #s(literal 1/4 binary64)))
(fma.f64 x #s(literal 1 binary64) (*.f64 y #s(literal -1/4 binary64)))
(fma.f64 x (/.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x))))
(fma.f64 x (/.f64 (.f64 x x) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))) (neg.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))))
(fma.f64 y #s(literal -1/4 binary64) x)
(fma.f64 y (/.f64 (.f64 y #s(literal 1/16 binary64)) (-.f64 (.f64 y #s(literal -1/4 binary64)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -1/4 binary64)) x))))
(fma.f64 (*.f64 y #s(literal 1/4 binary64)) #s(literal -1 binary64) x)
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (/.f64 (.f64 y #s(literal 1/4 binary64)) (-.f64 (.f64 y #s(literal -1/4 binary64)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (*.f64 y #s(literal -1/4 binary64)) x))))
(fma.f64 #s(literal -1/4 binary64) y x)
(fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 y (.f64 y #s(literal -1/4 binary64))) (-.f64 (.f64 y #s(literal -1/4 binary64)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (*.f64 y #s(literal -1/4 binary64)) x))))
(fma.f64 (.f64 y #s(literal -1/4 binary64)) (/.f64 (.f64 y #s(literal -1/4 binary64)) (-.f64 (.f64 y #s(literal -1/4 binary64)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (*.f64 y #s(literal -1/4 binary64)) x))))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))) (neg.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (*.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))))
(fma.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 y #s(literal -1/4 binary64)) x))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (neg.f64 (/.f64 (.f64 y (*.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x))))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))) (neg.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))))
(fma.f64 #s(literal 1 binary64) x (*.f64 y #s(literal -1/4 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 y #s(literal -1/4 binary64)) x)
(fma.f64 #s(literal 1/4 binary64) (neg.f64 y) x)
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 y #s(literal 1/4 binary64) x)) (/.f64 (.f64 x x) (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x)) (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x)))) (fma.f64 x (/.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (/.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (fma.f64 y #s(literal 1/4 binary64) x))))
(/.f64 (.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (*.f64 y #s(literal -1/4 binary64)) x))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))) (fma.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64) (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (.f64 x (.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))) (fma.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))) (fma.f64 x (.f64 x x) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/64 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 1/16 binary64) (.f64 x x)) (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 1/256 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 1/256 binary64)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 (.f64 y y) #s(literal 1/16 binary64) (.f64 x x)))
(/.f64 (.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (fma.f64 (.f64 y y) #s(literal 1/16 binary64) (.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 1/16 binary64) (.f64 x x)) (fma.f64 x x (.f64 (.f64 y y) #s(literal -1/16 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 (.f64 y y) #s(literal 1/16 binary64) (.f64 x x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (fma.f64 y #s(literal -1/4 binary64) x) (.f64 (-.f64 (*.f64 y #s(literal -1/4 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))))
(.f64 (fma.f64 y #s(literal -1/4 binary64) x) (/.f64 (-.f64 (.f64 y #s(literal -1/4 binary64)) x) (-.f64 (*.f64 y #s(literal -1/4 binary64)) x)))
(.f64 (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 (fma.f64 y #s(literal -1/4 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))))
(.f64 (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))) (/.f64 (fma.f64 y #s(literal -1/4 binary64) x) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (*.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))))
(*.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/4 binary64) x))
(.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 x x)) (/.f64 #s(literal -1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)))
(.f64 (fma.f64 x x (.f64 (*.f64 y y) #s(literal -1/16 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)))
(.f64 (fma.f64 y #s(literal 1/4 binary64) x) (.f64 (fma.f64 y #s(literal -1/4 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x))))
(*.f64 (fma.f64 y #s(literal 1/4 binary64) x) (/.f64 (fma.f64 y #s(literal -1/4 binary64) x) (fma.f64 y #s(literal 1/4 binary64) x)))
(.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (neg.f64 (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))))
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (*.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))) (fma.f64 x (.f64 x x) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/64 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 1/4 binary64) x)) (fma.f64 x x (.f64 (*.f64 y y) #s(literal -1/16 binary64))))
(.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal -1/16 binary64))) (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)))) (fma.f64 (.f64 y #s(literal 1/4 binary64)) (-.f64 (.f64 y #s(literal 1/4 binary64)) x) (.f64 x x)))
(.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal -1/16 binary64))) (fma.f64 x x (.f64 (*.f64 y y) #s(literal -1/16 binary64)))) (fma.f64 y #s(literal -1/4 binary64) x))
(.f64 (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 x x)) (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (*.f64 x x))) (fma.f64 y #s(literal -1/4 binary64) x))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))) (fma.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) #s(literal 1/4096 binary64) (.f64 (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)))))) (fma.f64 (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (-.f64 (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 y (.f64 y #s(literal 1/16 binary64)))) (.f64 (.f64 (.f64 y y) (*.f64 y y)) #s(literal 1/256 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))) (-.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 1/256 binary64)) (.f64 (.f64 x (fma.f64 y #s(literal 1/4 binary64) x)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))) (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (*.f64 x (fma.f64 y #s(literal 1/4 binary64) x))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))) (fma.f64 (.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 (fma.f64 y #s(literal 1/4 binary64) x) (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (-.f64 (.f64 y (.f64 #s(literal 1/4 binary64) (fma.f64 y #s(literal 1/4 binary64) x))) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64))) (.f64 (fma.f64 y (.f64 y #s(literal 1/16 binary64)) (.f64 x (fma.f64 y #s(literal 1/4 binary64) x))) (fma.f64 x x (.f64 (.f64 y #s(literal -1/4 binary64)) (fma.f64 y #s(literal 1/4 binary64) x))))) (fma.f64 x x (.f64 (.f64 y #s(literal -1/4 binary64)) (fma.f64 y #s(literal 1/4 binary64) x))))
(.f64 (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/16 binary64))) (.f64 x x)) (-.f64 (.f64 (.f64 y (.f64 y y)) #s(literal -1/64 binary64)) (.f64 x (.f64 x x)))) (fma.f64 x (fma.f64 y #s(literal -1/4 binary64) x) (.f64 y (*.f64 y #s(literal 1/16 binary64)))))

eval23.0ms (1%)

Memory: 1.7MiB live, 39.3MiB allocated
Compiler: Compiled 4 313 to 367 computations (91.5% saved)

prune24.0ms (1%)

Memory

13.9MiB live, 61.7MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	195	2	197

Accuracy

100.0%

Counts

197 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 y #s(literal -1/4 binary64) x)
✓	48.8%	#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Compiler

Compiled 27 to 16 computations (40.7% saved)

regimes9.0ms (0.4%)

Memory

-14.8MiB live, 24.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))
(fma.f64 y #s(literal -1/4 binary64) x)
(-.f64 x (/.f64 y #s(literal 4 binary64)))

Outputs
(fma.f64 y #s(literal -1/4 binary64) x)

Calls

4 calls:

3.0ms	(-.f64 x (/.f64 y #s(literal 4 binary64)))
2.0ms	(/.f64 y #s(literal 4 binary64))
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 x (/.f64 y #s(literal 4 binary64)))`
100.0%	1	`(/.f64 y #s(literal 4 binary64))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes6.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Outputs
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Calls

4 calls:

1.0ms	y
1.0ms	(-.f64 x (/.f64 y #s(literal 4 binary64)))
1.0ms	x
1.0ms	(/.f64 y #s(literal 4 binary64))

Results

Accuracy	Segments	Branch
48.8%	1	`x`
48.8%	1	`y`
48.8%	1	`(-.f64 x (/.f64 y #s(literal 4 binary64)))`
48.8%	1	`(/.f64 y #s(literal 4 binary64))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify6.0ms (0.3%)

Memory

-22.7MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	10	13

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 y #s(literal -1/4 binary64) x)
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

Outputs
(fma.f64 y #s(literal -1/4 binary64) x)
#s(approx (- x (/ y 4)) (*.f64 y #s(literal -1/4 binary64)))

soundness454.0ms (19.2%)

Memory

-10.9MiB live, 190.5MiB allocated

Rules

3 368×	`lower-fma.f64`
3 368×	`lower-fma.f32`
3 224×	`lower-*.f64`
3 224×	`lower-*.f32`
3 160×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
0	7	8
1	32	8
2	248	8
3	4066	8
0	8150	7
0	25	138
1	68	138
2	170	138
3	455	138
4	1251	138
5	2440	138
6	3244	138
7	3580	138
8	3876	138
9	4060	138
10	5213	138
11	6009	138
12	6777	138
13	7045	138
14	7825	138
0	8361	120

Stop Event

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

Compiler

Compiled 26 to 16 computations (38.5% saved)

preprocess48.0ms (2%)

Memory: 29.4MiB live, 73.4MiB allocated
Compiler: Compiled 34 to 20 computations (41.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	29
1	30	27
2	74	25
3	152	25
4	250	25
5	293	25
6	299	25
0	5	5
0	7	5
1	9	5
2	19	5
3	27	5
4	39	5
5	58	5
6	94	5
7	126	5
8	182	5
9	213	5
10	246	5
11	247	5
0	247	4

Iter	Nodes	Cost
0	5	11
0	7	11
1	9	11
2	19	11
3	27	11
4	39	11
5	58	11
6	94	11
7	126	11
8	182	11
9	213	11
10	246	11
11	247	11
0	247	10

Iter	Nodes	Cost
0	9	21
0	11	22
1	15	22
2	25	22
3	33	22
4	46	20
5	70	20
6	105	20
7	134	20
8	191	20
9	222	20
10	255	20
11	256	20
0	256	20

Iter	Nodes	Cost
0	13	29
1	30	27
2	74	25
3	152	25
4	250	25
5	293	25
6	299	25
0	5	5
0	7	5
1	9	5
2	19	5
3	27	5
4	39	5
5	58	5
6	94	5
7	126	5
8	182	5
9	213	5
10	246	5
11	247	5
0	247	4

Iter	Nodes	Cost
0	5	11
0	7	11
1	9	11
2	19	11
3	27	11
4	39	11
5	58	11
6	94	11
7	126	11
8	182	11
9	213	11
10	246	11
11	247	11
0	247	10

Iter	Nodes	Cost
0	9	21
0	11	22
1	15	22
2	25	22
3	33	22
4	46	20
5	70	20
6	105	20
7	134	20
8	191	20
9	222	20
10	255	20
11	256	20
0	256	20

start0.0ms (0%)

analyze0.0ms (0%)

sample699.0ms (29.5%)

explain48.0ms (2%)

preprocess33.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify10.0ms (0.4%)

localize16.0ms (0.7%)

series3.0ms (0.1%)

simplify227.0ms (9.6%)

rewrite189.0ms (8%)

eval50.0ms (2.1%)

prune19.0ms (0.8%)

simplify15.0ms (0.6%)

localize24.0ms (1%)

series2.0ms (0.1%)

simplify260.0ms (11%)

rewrite200.0ms (8.5%)

eval23.0ms (1%)

prune24.0ms (1%)

regimes9.0ms (0.4%)

regimes6.0ms (0.2%)

simplify6.0ms (0.3%)

soundness454.0ms (19.2%)

preprocess48.0ms (2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	29
1	30	27
2	74	25
3	152	25
4	250	25
5	293	25
6	299	25
0	5	5
0	7	5
1	9	5
2	19	5
3	27	5
4	39	5
5	58	5
6	94	5
7	126	5
8	182	5
9	213	5
10	246	5
11	247	5
0	247	4

Iter	Nodes	Cost
0	5	11
0	7	11
1	9	11
2	19	11
3	27	11
4	39	11
5	58	11
6	94	11
7	126	11
8	182	11
9	213	11
10	246	11
11	247	11
0	247	10

Iter	Nodes	Cost
0	9	21
0	11	22
1	15	22
2	25	22
3	33	22
4	46	20
5	70	20
6	105	20
7	134	20
8	191	20
9	222	20
10	255	20
11	256	20
0	256	20