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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample538.0ms (27.6%)

Memory

-14.1MiB live, 874.6MiB allocated

Samples

334.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-div: 69.0ms (50.7% of total)

ival-sub: 54.0ms (39.7% of total)

ival-true: 6.0ms (4.4% of total)

exact: 4.0ms (2.9% of total)

ival-assert: 3.0ms (2.2% of total)

Bogosity

explain48.0ms (2.4%)

Memory

19.5MiB live, 58.2MiB 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

18.0ms

512×

valid

Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (44.3% of total)

ival-sub: 2.0ms (29.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess31.0ms (1.6%)

Memory

-9.0MiB live, 28.9MiB 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 #s(literal -1/4 binary64) y x)

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 5 computations (0% saved)

simplify9.0ms (0.4%)

Memory

6.5MiB live, 6.5MiB 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 #s(literal -1/4 binary64) y x)
x
(/.f64 y #s(literal 4 binary64))
(*.f64 #s(literal 1/4 binary64) y)
y
#s(literal 4 binary64)

localize22.0ms (1.1%)

Memory

-17.6MiB live, 19.1MiB 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

8.0ms

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 (62.6% of total)

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

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.2%)

Memory

5.3MiB live, 5.3MiB 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 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 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 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 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 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>) () ())) ())
#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>) () ())) ())

Calls

6 calls:

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

simplify180.0ms (9.2%)

Memory

10.7MiB live, 94.5MiB 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	1249	138
5	2477	138
6	3282	138
7	3618	138
8	3914	138
9	4095	138
10	5236	138
11	6032	138
12	6800	138
13	7068	138
14	7848	138
0	8384	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)
x
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(+ x (* -1/4 y))
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* -1/4 y)
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* y (- (/ x y) 1/4))
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* 1/4 y)
(* -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 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
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 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* -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 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* 1/4 y)
(*.f64 y #s(literal 1/4 binary64))
(* -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)

rewrite187.0ms (9.6%)

Memory

-7.7MiB live, 193.9MiB 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
(*.f64 (exp.f64 (log.f64 #s(literal 1/4 binary64))) (exp.f64 (log.f64 y)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 #s(literal 1/4 binary64))))
(*.f64 (exp.f64 (log.f64 (neg.f64 y))) (exp.f64 (log.f64 #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (pow.f64 (neg.f64 y) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/4 binary64))
(*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 y) #s(literal 1 binary64)) #s(literal -1/4 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal -1/4 binary64) (pow.f64 (pow.f64 (neg.f64 y) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/4 binary64) (pow.f64 (neg.f64 y) #s(literal 1 binary64)))
(*.f64 #s(literal -1/4 binary64) (neg.f64 y))
(.f64 #s(literal -1 binary64) (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -1/4 binary64) y))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 1 binary64)))
(*.f64 #s(literal 1/4 binary64) y)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) y))
(*.f64 (neg.f64 y) #s(literal -1/4 binary64))
(.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 1 binary64))
(*.f64 y #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) y)))
(pow.f64 (pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal -1/4 binary64) y) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) y) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/4 binary64) y) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 #s(literal -4 binary64) y))))
(/.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 #s(literal 4 binary64))))
(/.f64 (exp.f64 (log.f64 (neg.f64 y))) (exp.f64 (log.f64 #s(literal -4 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) y))
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(fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal -1/16 binary64) (.f64 x x))) (fma.f64 #s(literal -1/4 binary64) y x) (neg.f64 (.f64 (*.f64 y y) (/.f64 #s(literal 1/16 binary64) (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/16 binary64) (pow.f64 (.f64 y (fma.f64 #s(literal 1/4 binary64) y x)) #s(literal 2 binary64))))) (fma.f64 x x (.f64 (.f64 #s(literal -1/4 binary64) y) (fma.f64 #s(literal 1/4 binary64) y x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (*.f64 x x)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 (.f64 y (fma.f64 #s(literal 1/4 binary64) y x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y)) (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (*.f64 x x)))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (*.f64 x x)))))
(fma.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/4 binary64) y x)
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/4 binary64) y) x)
(fma.f64 #s(literal 1/4 binary64) (pow.f64 (neg.f64 (pow.f64 y #s(literal -1 binary64))) #s(literal -1 binary64)) x)
(fma.f64 #s(literal 1/4 binary64) (neg.f64 y) x)
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) y) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal -1/4 binary64) y))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x)))))
(fma.f64 (.f64 x x) (pow.f64 (fma.f64 #s(literal 1/4 binary64) y x) #s(literal -1 binary64)) (neg.f64 (.f64 (*.f64 y y) (/.f64 #s(literal 1/16 binary64) (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (*.f64 x x)))))
(fma.f64 (neg.f64 y) #s(literal 1/4 binary64) x)
(fma.f64 x (/.f64 x (fma.f64 #s(literal 1/4 binary64) y x)) (neg.f64 (.f64 (.f64 y y) (/.f64 #s(literal 1/16 binary64) (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 x (/.f64 (.f64 x x) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x)))))
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) y))
(fma.f64 (*.f64 #s(literal 1/4 binary64) y) #s(literal -1 binary64) x)
(fma.f64 y #s(literal -1/4 binary64) x)
(-.f64 (+.f64 x #s(literal 0 binary64)) (*.f64 #s(literal 1/4 binary64) y))
(-.f64 (.f64 x (/.f64 x (fma.f64 #s(literal 1/4 binary64) y x))) (.f64 (*.f64 y y) (/.f64 #s(literal 1/16 binary64) (fma.f64 #s(literal 1/4 binary64) y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x))) (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) y) x))
(-.f64 x (*.f64 #s(literal 1/4 binary64) y))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 #s(literal -1/4 binary64) y x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 x (/.f64 x (fma.f64 #s(literal 1/4 binary64) y x))) (neg.f64 (.f64 (*.f64 y y) (/.f64 #s(literal 1/16 binary64) (fma.f64 #s(literal 1/4 binary64) y x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y) (*.f64 x x)))))
(+.f64 (*.f64 #s(literal -1/4 binary64) y) x)
(+.f64 x (*.f64 #s(literal -1/4 binary64) y))

eval19.0ms (1%)

Memory: 5.1MiB live, 43.0MiB allocated
Compiler: Compiled 2 670 to 398 computations (85.1% saved)

prune4.0ms (0.2%)

Memory

13.4MiB live, 13.4MiB 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)
▶	51.8%	#s(approx (- x (/ y 4)) (*.f64 #s(literal -1/4 binary64) y))

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify24.0ms (1.2%)

Memory

-37.9MiB live, 9.1MiB 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 #s(literal -1/4 binary64) y)
cost-diff	0	#s(approx (- x (/ y 4)) (*.f64 #s(literal -1/4 binary64) y))

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	12	21
1	16	21
2	26	21
3	34	21
4	47	20
5	71	20
6	106	20
7	135	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 #s(literal -1/4 binary64) y))
(*.f64 #s(literal -1/4 binary64) y)
#s(literal -1/4 binary64)
y
(fma.f64 y #s(literal -1/4 binary64) x)
y
#s(literal -1/4 binary64)
x

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

localize20.0ms (1%)

Memory

31.9MiB live, 31.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y #s(literal -1/4 binary64) x)
accuracy	0	(*.f64 #s(literal -1/4 binary64) y)
accuracy	30.876762357458293	#s(approx (- x (/ y 4)) (*.f64 #s(literal -1/4 binary64) y))

Samples

14.0ms

256×

valid

Compiler

Compiled 20 to 11 computations (45% saved)

Precisions

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

ival-mult: 3.0ms (39.9% of total)

ival-div: 2.0ms (26.6% of total)

ival-sub: 1.0ms (13.3% of total)

ival-add: 1.0ms (13.3% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.8%)

Memory

-31.3MiB live, 7.8MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs

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

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

6 calls:

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

simplify193.0ms (9.9%)

Memory

25.9MiB live, 144.3MiB 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	456	240
4	1244	240
5	2466	240
6	3268	240
7	3604	240
8	3900	240
9	4084	240
10	5232	240
11	6028	240
12	6796	240
13	7064	240
14	7844	240
0	8380	204

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

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

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

rewrite121.0ms (6.2%)

Memory

-2.8MiB live, 188.3MiB 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	12	16
1	49	15
2	399	15
3	6477	15
0	8203	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 #s(literal -1/4 binary64) y))
(*.f64 #s(literal -1/4 binary64) y)
(fma.f64 y #s(literal -1/4 binary64) x)

Outputs
#s(approx (- x (/ y 4)) (*.f64 #s(literal -1/4 binary64) y))
(*.f64 (neg.f64 y) #s(literal 1/4 binary64))
(.f64 #s(literal -1 binary64) (.f64 #s(literal 1/4 binary64) y))
(*.f64 #s(literal 1/4 binary64) (neg.f64 y))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -1/4 binary64) y))
(*.f64 #s(literal -1/4 binary64) y)
(.f64 (.f64 #s(literal 1/4 binary64) y) #s(literal -1 binary64))
(*.f64 y #s(literal -1/4 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))
(pow.f64 (/.f64 #s(literal -4 binary64) y) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal -1/4 binary64) y) #s(literal 1 binary64))
(/.f64 (.f64 #s(literal -1/16 binary64) (.f64 y y)) (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) y)))
(/.f64 (neg.f64 y) #s(literal 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 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) y)))))
(/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal -1 binary64)))
(/.f64 y #s(literal -4 binary64))
(neg.f64 (*.f64 #s(literal 1/4 binary64) y))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/4 binary64) y))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -4 binary64) y)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal -1/4 binary64) y)) #s(literal 1 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/4 binary64) y))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (neg.f64 x) x)) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/16 binary64) (.f64 y y) (*.f64 x (fma.f64 #s(literal -1/4 binary64) y x))))
(.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y)) #s(literal 2 binary64)))) (fma.f64 x x (.f64 (*.f64 #s(literal -1/4 binary64) y) (fma.f64 #s(literal 1/4 binary64) y x))))
(.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y)) (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 #s(literal 1/4 binary64) y)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (/.f64 #s(literal -4 binary64) y) #s(literal -4 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)))
(.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4096 binary64) (pow.f64 y #s(literal 6 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x) #s(literal 3 binary64)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x) (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x) (pow.f64 (*.f64 #s(literal -1/4 binary64) y) #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal -4 binary64) y) #s(literal -4 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (neg.f64 x) x)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (neg.f64 x) x))) (fma.f64 #s(literal -1/4 binary64) y x))
(.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 y y) (.f64 x x)) (fma.f64 #s(literal -1/16 binary64) (.f64 y y) (*.f64 x x))) (fma.f64 #s(literal -1/4 binary64) y x))
(.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 y y) (.f64 x x)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) y) (-.f64 (.f64 #s(literal 1/4 binary64) y) x) (.f64 x x)))
(.f64 (pow.f64 (fma.f64 #s(literal 1/4 binary64) y x) #s(literal -1 binary64)) (fma.f64 #s(literal -1/16 binary64) (.f64 y y) (*.f64 x x)))
(.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) y x)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (neg.f64 x) x)))
(.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 1/4 binary64) y x) (/.f64 (fma.f64 #s(literal -1/4 binary64) y x) (fma.f64 #s(literal 1/4 binary64) y x)))
(.f64 (fma.f64 #s(literal 1/4 binary64) y x) (.f64 (fma.f64 #s(literal -1/4 binary64) y x) (pow.f64 (fma.f64 #s(literal 1/4 binary64) y x) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 y y) (*.f64 x x)) (pow.f64 (fma.f64 #s(literal 1/4 binary64) y x) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (neg.f64 x) x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) y x)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/4 binary64) y x))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)) (/.f64 (fma.f64 #s(literal -1/4 binary64) y x) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)) (.f64 (fma.f64 #s(literal -1/4 binary64) y x) (pow.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/4 binary64) y x) (/.f64 (-.f64 (.f64 #s(literal -1/4 binary64) y) x) (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))
(.f64 (fma.f64 #s(literal -1/4 binary64) y x) (.f64 (-.f64 (*.f64 #s(literal -1/4 binary64) y) x) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) y x))))
(pow.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/4 binary64) y x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal -1/4 binary64) y x) #s(literal -1 binary64)) #s(literal -1 binary64))
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(fma.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) y) (-.f64 (.f64 #s(literal 1/4 binary64) y) x) (.f64 x x)) (neg.f64 (.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/16 binary64) (.f64 y y) (.f64 x x))) (fma.f64 #s(literal -1/4 binary64) y x) (neg.f64 (.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (/.f64 #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 y y) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)))))
(fma.f64 (neg.f64 y) #s(literal 1/4 binary64) x)
(fma.f64 (.f64 y y) (/.f64 #s(literal 1/16 binary64) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/4 binary64) y) x)
(fma.f64 #s(literal 1/4 binary64) (neg.f64 y) x)
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) y) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal -1/4 binary64) y))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)))))
(fma.f64 (.f64 x x) (pow.f64 (fma.f64 #s(literal 1/4 binary64) y x) #s(literal -1 binary64)) (neg.f64 (.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/4 binary64) y x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)))))
(fma.f64 (.f64 #s(literal -1/4 binary64) y) (/.f64 (.f64 #s(literal -1/4 binary64) y) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 y y) #s(literal -1/4 binary64)) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 #s(literal -1/4 binary64) y x)
(fma.f64 (.f64 #s(literal 1/4 binary64) y) (/.f64 (.f64 #s(literal 1/4 binary64) y) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 (*.f64 #s(literal 1/4 binary64) y) #s(literal -1 binary64) x)
(fma.f64 y (/.f64 (.f64 #s(literal 1/16 binary64) y) (-.f64 (.f64 #s(literal -1/4 binary64) y) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) y) x)))))
(fma.f64 y #s(literal -1/4 binary64) x)
(fma.f64 x (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)))))
(fma.f64 x (/.f64 x (fma.f64 #s(literal 1/4 binary64) y x)) (neg.f64 (.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (fma.f64 #s(literal 1/4 binary64) y x)))))
(fma.f64 x #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) y))
(-.f64 (+.f64 x #s(literal 0 binary64)) (*.f64 #s(literal 1/4 binary64) y))
(-.f64 (.f64 x (/.f64 x (fma.f64 #s(literal 1/4 binary64) y x))) (.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (fma.f64 #s(literal 1/4 binary64) y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))) (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))))
(-.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 y y)) (fma.f64 #s(literal 1/4 binary64) y x)) (.f64 x (/.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) y) x))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 1/4 binary64) y) x))
(-.f64 x (*.f64 #s(literal 1/4 binary64) y))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 #s(literal -1/4 binary64) y x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 x (/.f64 x (fma.f64 #s(literal 1/4 binary64) y x))) (neg.f64 (.f64 (*.f64 #s(literal 1/16 binary64) y) (/.f64 y (fma.f64 #s(literal 1/4 binary64) y x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (.f64 (fma.f64 #s(literal 1/4 binary64) y x) x))) (neg.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) y) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) y) y (*.f64 (fma.f64 #s(literal 1/4 binary64) y x) x)))))
(+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 y y)) (fma.f64 #s(literal 1/4 binary64) y x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 #s(literal -1/4 binary64) y) x)))))
(+.f64 (*.f64 #s(literal -1/4 binary64) y) x)
(+.f64 x (*.f64 #s(literal -1/4 binary64) y))

eval22.0ms (1.1%)

Memory: 23.2MiB live, 60.3MiB allocated
Compiler: Compiled 3 387 to 411 computations (87.9% saved)

prune9.0ms (0.5%)

Memory

-10.5MiB live, 26.4MiB 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)
✓	51.8%	#s(approx (- x (/ y 4)) (*.f64 #s(literal -1/4 binary64) y))

Compiler

Compiled 21 to 18 computations (14.3% saved)

regimes47.0ms (2.4%)

Memory

-22.6MiB live, 61.0MiB allocated

Counts

3 → 1

Calls

Call 1

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

41.0ms	x
2.0ms	(/.f64 y #s(literal 4 binary64))
2.0ms	(-.f64 x (/.f64 y #s(literal 4 binary64)))
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 10 to 13 computations (-30% saved)

regimes5.0ms (0.3%)

Memory

17.2MiB live, 17.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
51.8%	1	`x`
51.8%	1	`y`
51.8%	1	`(-.f64 x (/.f64 y #s(literal 4 binary64)))`
51.8%	1	`(/.f64 y #s(literal 4 binary64))`

Compiler

Compiled 10 to 13 computations (-30% saved)

simplify26.0ms (1.3%)

Memory

8.0MiB live, 80.1MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

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 #s(literal -1/4 binary64) y))

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

soundness405.0ms (20.8%)

Memory

4.7MiB live, 248.2MiB 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	1249	138
5	2477	138
6	3282	138
7	3618	138
8	3914	138
9	4095	138
10	5236	138
11	6032	138
12	6800	138
13	7068	138
14	7848	138
0	8384	120

Stop Event

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

Compiler

Compiled 20 to 17 computations (15% saved)

preprocess22.0ms (1.1%)

Memory: -17.0MiB live, 59.8MiB allocated
Compiler: Compiled 26 to 22 computations (15.4% 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	12	21
1	16	21
2	26	21
3	34	21
4	47	20
5	71	20
6	106	20
7	135	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	12	21
1	16	21
2	26	21
3	34	21
4	47	20
5	71	20
6	106	20
7	135	20
8	191	20
9	222	20
10	255	20
11	256	20
0	256	20

start0.0ms (0%)

analyze0.0ms (0%)

sample538.0ms (27.6%)

explain48.0ms (2.4%)

preprocess31.0ms (1.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.4%)

localize22.0ms (1.1%)

series3.0ms (0.2%)

simplify180.0ms (9.2%)

rewrite187.0ms (9.6%)

eval19.0ms (1%)

prune4.0ms (0.2%)

simplify24.0ms (1.2%)

localize20.0ms (1%)

series16.0ms (0.8%)

simplify193.0ms (9.9%)

rewrite121.0ms (6.2%)

eval22.0ms (1.1%)

prune9.0ms (0.5%)

regimes47.0ms (2.4%)

regimes5.0ms (0.3%)

simplify26.0ms (1.3%)

soundness405.0ms (20.8%)

preprocess22.0ms (1.1%)

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	12	21
1	16	21
2	26	21
3	34	21
4	47	20
5	71	20
6	106	20
7	135	20
8	191	20
9	222	20
10	255	20
11	256	20
0	256	20