Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

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 9 to 7 computations (22.2% saved)

sample682.0ms (27.7%)

Memory

-22.5MiB live, 1 327.4MiB allocated

Samples

452.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 220.0ms

ival-add: 119.0ms (54.1% of total)

ival-mult: 91.0ms (41.4% of total)

ival-true: 6.0ms (2.7% of total)

ival-assert: 4.0ms (1.8% of total)

Bogosity

explain64.0ms (2.6%)

Memory

12.9MiB live, 174.2MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (*.f64 x x) y)`
-	-	`(+.f64 (+.f64 (*.f64 x x) y) y)`
-	-	`y`
-	-	`(*.f64 x x)`
-	-	`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

21.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

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

ival-add: 4.0ms (44.8% of total)

ival-mult: 4.0ms (44.8% of total)

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

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

preprocess26.0ms (1%)

Memory

8.0MiB live, 46.5MiB allocated

Algorithm

1×	egg-herbie

Rules

118×	`sub-neg`
108×	`unsub-neg`
72×	`associate-+l-`
64×	`distribute-rgt-in`
58×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

Stop Event

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

Calls

Call 1

Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)

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

Symmetry

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.f64 (+.f64 (*.f64 x x) y) y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (*.f64 x x) y)

Rules

14×	`lower-+.f32`
10×	`lower-+.f64`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
6×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	12	17
2	15	17
3	16	17
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

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

localize18.0ms (0.7%)

Memory

-4.6MiB live, 36.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (*.f64 x x) y)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (+.f64 (*.f64 x x) y) y)

Samples

12.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-mult: 4.0ms (64.3% of total)

ival-add: 2.0ms (32.2% of total)

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

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

series4.0ms (0.2%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())

Inputs

#s(alt (+.f64 (*.f64 x x) y) (patch (+.f64 (*.f64 x x) y) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

#s(alt (+.f64 (+.f64 (*.f64 x x) y) y) (patch (+.f64 (+.f64 (*.f64 x x) y) y) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2))) (taylor -inf y) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) y) y) (patch (+.f64 (+.f64 (.f64 x x) y) y) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify97.0ms (3.9%)

Memory

-39.6MiB live, 163.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4 690×	`lower-fma.f64`
4 690×	`lower-fma.f32`
3 340×	`lower-*.f64`
3 340×	`lower-*.f32`
1 326×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	282
1	80	282
2	193	282
3	649	282
4	1930	282
5	3616	282
6	6722	282
0	8178	246

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 57

Calls

Call 1

Inputs
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))

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

rewrite169.0ms (6.9%)

Memory

42.4MiB live, 229.5MiB allocated

Rules

7 306×	`lower-fma.f64`
7 306×	`lower-fma.f32`
4 782×	`lower-*.f32`
4 780×	`lower-*.f64`
2 300×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	37	15
2	316	15
3	4987	15
0	8103	13

Stop Event

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

Counts

3 → 251

Calls

Call 1

Inputs
(+.f64 (*.f64 x x) y)
(*.f64 x x)
(+.f64 (+.f64 (*.f64 x x) y) y)

Outputs
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eval40.0ms (1.6%)

Memory: -1.6MiB live, 84.4MiB allocated
Compiler: Compiled 5 874 to 711 computations (87.9% saved)

prune10.0ms (0.4%)

Memory

-8.1MiB live, 29.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	303	5	308
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	304	5	309

Accuracy

100.0%

Counts

309 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
▶	100.0%	(+.f64 (fma.f64 x x y) y)
▶	60.8%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
▶	48.7%	#s(approx (+ (+ (* x x) y) y) (*.f64 y #s(literal 2 binary64)))
▶	53.5%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 52 to 46 computations (11.5% saved)

simplify5.0ms (0.2%)

Memory

6.4MiB live, 6.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.f64 (fma.f64 x x y) y)
cost-diff	0	(fma.f64 x x y)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) y) (*.f64 x x))
cost-diff	0	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
cost-diff	0	(*.f64 y #s(literal 2 binary64))
cost-diff	0	#s(approx (+ (+ (* x x) y) y) (*.f64 y #s(literal 2 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y #s(literal 2 binary64) (*.f64 x x))

Rules

18×	`lower-+.f32`
14×	`lower-+.f64`
8×	`lower-fma.f32`
8×	`+-commutative`
6×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	76
0	21	76
1	28	76
2	28	76
0	28	76

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (1.1%)

Memory

4.7MiB live, 42.5MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	0.0078125	(+.f64 (fma.f64 x x y) y)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
accuracy	29.77999632171359	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	32.80476884100121	#s(approx (+ (+ (* x x) y) y) (*.f64 y #s(literal 2 binary64)))
accuracy	0	(*.f64 x x)
accuracy	29.785735278005692	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
accuracy	0	(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
accuracy	0	(*.f64 x x)

Samples

20.0ms

256×

valid

Compiler

Compiled 69 to 10 computations (85.5% saved)

Precisions

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

ival-add: 3.0ms (43.5% of total)

ival-mult: 3.0ms (43.5% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.5%)

Memory

-24.0MiB live, 13.2MiB allocated

Counts

9 → 192

Calls

Call 1

Inputs
#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())
#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 2 binary64)) (patch (.f64 y #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 y #s(literal 2 binary64) (.f64 x x)) (patch (fma.f64 y #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 x x)) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (.f64 y #s(literal 2 binary64))) (patch #s(approx (+ (+ ( x x) y) y) (*.f64 y #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (patch (+.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (fma.f64 x x y) y) (patch (+.f64 (fma.f64 x x y) y) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify107.0ms (4.3%)

Memory

-3.1MiB live, 115.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4 690×	`lower-fma.f64`
4 690×	`lower-fma.f32`
3 340×	`lower-*.f64`
3 340×	`lower-*.f32`
1 326×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	996
1	80	996
2	193	996
3	651	996
4	1923	996
5	3631	996
6	6729	996
0	8179	870

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 186

Calls

Call 1

Inputs
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))

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

rewrite178.0ms (7.2%)

Memory

5.2MiB live, 249.2MiB allocated

Rules

9 808×	`lower-fma.f32`
9 804×	`lower-fma.f64`
4 678×	`lower-*.f32`
4 674×	`lower-*.f64`
3 512×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	60
0	21	60
1	72	60
2	562	60
0	8080	60

Stop Event

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

Counts

9 → 745

Calls

Call 1

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

Outputs
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eval112.0ms (4.5%)

Memory: 26.1MiB live, 175.0MiB allocated
Compiler: Compiled 14 726 to 1 186 computations (91.9% saved)

prune22.0ms (0.9%)

Memory

-12.6MiB live, 61.7MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	966	1	967
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	967	5	972

Accuracy

100.0%

Counts

972 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
✓	100.0%	(+.f64 (fma.f64 x x y) y)
✓	60.8%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
▶	48.7%	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
✓	53.5%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify4.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	-128	(+.f64 y y)
cost-diff	0	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Rules

14×	`lower-+.f32`
12×	`lower-+.f64`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
6×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
0	8	15
1	13	15
2	15	15
0	15	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
(+.f64 y y)
y

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

localize17.0ms (0.7%)

Memory

-0.4MiB live, 37.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 y y)
accuracy	32.80476884100121	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Samples

13.0ms

256×

valid

Compiler

Compiled 13 to 8 computations (38.5% saved)

Precisions

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

ival-add: 3.0ms (54.2% of total)

ival-mult: 2.0ms (36.1% of total)

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

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

series3.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs

#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())

#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 2 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2))) (taylor -inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2))) (taylor -inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2))) (taylor -inf y) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor -inf y) (#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* 2 y) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 y) (pow x 2)) (taylor 0 x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) (patch #s(approx (+ (+ (* x x) y) y) (+.f64 y y)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify88.0ms (3.6%)

Memory

-17.8MiB live, 106.0MiB allocated

Algorithm

1×	egg-herbie

Rules

3 234×	`lower-fma.f64`
3 234×	`lower-fma.f32`
3 064×	`lower-*.f64`
3 064×	`lower-*.f32`
1 974×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	180
1	53	180
2	130	180
3	426	180
4	1329	180
5	3258	180
6	6178	180
0	8055	162

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))

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

rewrite40.0ms (1.6%)

Memory

12.1MiB live, 50.7MiB allocated

Rules

188×	`lower-fma.f64`
188×	`lower-fma.f32`
170×	`lower-*.f64`
170×	`lower-*.f32`
150×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
0	8	14
1	43	14
0	376	13

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 12

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
(+.f64 y y)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval4.0ms (0.2%)

Memory: 8.3MiB live, 8.3MiB allocated
Compiler: Compiled 304 to 44 computations (85.5% saved)

prune3.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	48	5	53

Accuracy

100.0%

Counts

53 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
✓	100.0%	(+.f64 (fma.f64 x x y) y)
✓	60.8%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
✓	48.7%	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
✓	53.5%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 63 to 38 computations (39.7% saved)

regimes43.0ms (1.7%)

Memory

-25.4MiB live, 41.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

11.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
3.0ms	y
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes14.0ms (0.6%)

Memory

-18.9MiB live, 18.5MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs
(+.f64 (fma.f64 x x y) y)

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
3.0ms	y
3.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes9.0ms (0.4%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)

Calls

4 calls:

2.0ms	y
2.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
2.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.4%	2	`x`
72.6%	3	`y`
81.0%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
88.4%	2	`(*.f64 x x)`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes4.0ms (0.2%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

3 → 2

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Calls

2 calls:

2.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
86.8%	2	`x`
86.8%	2	`(*.f64 x x)`

Compiler

Compiled 4 to 5 computations (-25% saved)

regimes7.0ms (0.3%)

Memory

-27.1MiB live, 11.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Outputs
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Calls

4 calls:

3.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	y
1.0ms	x
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
48.7%	1	`y`
48.7%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
48.7%	1	`x`
48.7%	1	`(*.f64 x x)`

Compiler

Compiled 12 to 12 computations (0% saved)

bsearch9.0ms (0.4%)

Memory

12.2MiB live, 12.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	2.7336057163622108e-101	5.467655874588128e-97

Samples

4.0ms

128×

valid

Compiler

Compiled 74 to 90 computations (-21.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add: 1.0ms (72.8% of total)

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

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

bsearch10.0ms (0.4%)

Memory

13.6MiB live, 13.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.0286358448779193e-50	6.817158031618037e-44

Samples

4.0ms

144×

valid

Compiler

Compiled 64 to 91 computations (-42.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (64.4% of total)

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

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

simplify28.0ms (1.1%)

Memory

-25.3MiB live, 55.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	79
1	23	79

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(if (<=.f64 (.f64 x x) #s(literal 8003532508642629/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) (+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y))
(if (<=.f64 (.f64 x x) #s(literal 1349313737003389/3291009114642412084309938365114701009965471731267159726697218048 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) #s(approx (+ (+ (* x x) y) y) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Outputs
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(if (<=.f64 (.f64 x x) #s(literal 8003532508642629/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) (+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y))
(if (<=.f64 (.f64 x x) #s(literal 1349313737003389/3291009114642412084309938365114701009965471731267159726697218048 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) #s(approx (+ (+ (* x x) y) y) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

soundness528.0ms (21.4%)

Memory

19.0MiB live, 285.5MiB allocated

Rules

9 808×	`lower-fma.f32`
9 804×	`lower-fma.f64`
7 306×	`lower-fma.f64`
7 306×	`lower-fma.f32`
4 782×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	282
1	80	282
2	193	282
3	649	282
4	1930	282
5	3616	282
6	6722	282
0	8178	246
0	5	15
0	8	15
1	37	15
2	316	15
3	4987	15
0	8103	13
0	15	60
0	21	60
1	72	60
2	562	60
0	8080	60

Stop Event

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

Compiler

Compiled 101 to 66 computations (34.7% saved)

preprocess76.0ms (3.1%)

Memory: 15.6MiB live, 135.0MiB allocated
Remove: (abs x)
Compiler: Compiled 132 to 66 computations (50% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

start0.0ms (0%)

analyze0.0ms (0%)

sample682.0ms (27.7%)

explain64.0ms (2.6%)

preprocess26.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize18.0ms (0.7%)

series4.0ms (0.2%)

simplify97.0ms (3.9%)

rewrite169.0ms (6.9%)

eval40.0ms (1.6%)

prune10.0ms (0.4%)

simplify5.0ms (0.2%)

localize28.0ms (1.1%)

series12.0ms (0.5%)

simplify107.0ms (4.3%)

rewrite178.0ms (7.2%)

eval112.0ms (4.5%)

prune22.0ms (0.9%)

simplify4.0ms (0.2%)

localize17.0ms (0.7%)

series3.0ms (0.1%)

simplify88.0ms (3.6%)

rewrite40.0ms (1.6%)

eval4.0ms (0.2%)

prune3.0ms (0.1%)

regimes43.0ms (1.7%)

regimes14.0ms (0.6%)

regimes9.0ms (0.4%)

regimes4.0ms (0.2%)

regimes7.0ms (0.3%)

bsearch9.0ms (0.4%)

bsearch10.0ms (0.4%)

simplify28.0ms (1.1%)

soundness528.0ms (21.4%)

preprocess76.0ms (3.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6