Metrics for Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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 11 to 10 computations (9.1% saved)

sample1.1s (24.3%)

Memory

17.8MiB live, 1 208.2MiB allocated

Samples

680.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 381.0ms

ival-add: 203.0ms (53.3% of total)

ival-div: 97.0ms (25.5% of total)

ival-mult: 66.0ms (17.3% of total)

ival-true: 7.0ms (1.8% of total)

exact: 5.0ms (1.3% of total)

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

Bogosity

explain188.0ms (4.3%)

Memory

14.2MiB live, 174.6MiB allocated

FPErrors

Click to see full error table

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

135.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-div: 6.0ms (40.1% of total)

ival-add: 5.0ms (33.4% of total)

ival-mult: 4.0ms (26.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess422.0ms (9.6%)

Memory

-15.4MiB live, 61.1MiB allocated

Algorithm

1×	egg-herbie

Rules

386×	`distribute-rgt-in`
336×	`sub-neg`
268×	`unsub-neg`
230×	`associate-+l-`
226×	`cancel-sign-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	88
1	88	82
2	232	81
3	662	69
4	1166	65
5	1714	63
6	2190	63
7	2376	63
8	2424	63
9	2432	63
10	2432	63
0	8	9
0	12	9
1	17	9
2	24	9
3	26	9
0	26	8

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify4.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

24×	`lower-+.f32`
20×	`lower-+.f64`
12×	`lower-fma.f64`
12×	`lower-fma.f32`
10×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
0	12	26
1	17	26
2	24	26
3	26	26
0	26	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize24.0ms (0.6%)

Memory

6.4MiB live, 43.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x #s(literal 2 binary64))
accuracy	0	(*.f64 y x)
accuracy	0.00390625	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
accuracy	0.00390625	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Samples

19.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

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

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

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

ival-mult: 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)

series29.0ms (0.6%)

Memory

-25.0MiB live, 18.5MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) (patch (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) #<representation binary64>) () ())
#s(alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) z) (patch (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) z) #<representation binary64>) () ())
#s(alt (/.f64 x #s(literal 2 binary64)) (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
18.0ms	x	@	inf	((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
5.0ms	x	@	-inf	((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
1.0ms	y	@	-inf	((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
1.0ms	x	@	0	((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))
0.0ms	y	@	inf	((+ (/ x 2) (* y x)) (+ (+ (/ x 2) (* y x)) z) (/ x 2) (* y x))

simplify115.0ms (2.6%)

Memory

7.8MiB live, 171.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 434×	`lower-fma.f64`
6 434×	`lower-fma.f32`
2 474×	`lower-*.f64`
2 474×	`lower-*.f32`
1 356×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	440
1	174	440
2	488	440
3	1308	440
4	3609	440
5	6674	440
0	8210	412

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 93

Calls

Call 1

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

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

rewrite164.0ms (3.7%)

Memory

9.2MiB live, 317.2MiB allocated

Rules

7 074×	`lower-fma.f64`
7 074×	`lower-fma.f32`
4 356×	`lower-*.f32`
4 354×	`lower-*.f64`
2 578×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
0	12	22
1	52	18
2	452	18
3	6077	18
0	8040	17

Stop Event

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

Counts

4 → 242

Calls

Call 1

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

Outputs
#<batchref>
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eval39.0ms (0.9%)

Memory: 20.6MiB live, 137.8MiB allocated
Compiler: Compiled 6 518 to 757 computations (88.4% saved)

prune9.0ms (0.2%)

Memory

-12.9MiB live, 32.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	330	5	335
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	331	5	336

Accuracy

100.0%

Counts

336 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
▶	71.8%	(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
▶	69.2%	#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
▶	60.5%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
▶	32.4%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

Compiler

Compiled 54 to 60 computations (-11.1% saved)

simplify6.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y x)
cost-diff	0	#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
cost-diff	0	(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
cost-diff	0	(-.f64 y #s(literal -1/2 binary64))
cost-diff	0	(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
cost-diff	0	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) z)
cost-diff	0	#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
cost-diff	0	(*.f64 y x)
cost-diff	0	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
cost-diff	0	(+.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)

Rules

52×	`lower-+.f32`
48×	`lower-+.f64`
36×	`lower-fma.f32`
32×	`lower-fma.f64`
18×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	108
0	30	108
1	44	108
2	53	108
3	59	108
0	59	103

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (1%)

Memory

0.8MiB live, 77.7MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y x)
accuracy	0.00390625	(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
accuracy	33.8762555862769	#s(approx (+ (/ x 2) (* y x)) (*.f64 y x))
accuracy	0	(-.f64 y #s(literal -1/2 binary64))
accuracy	0	(*.f64 (-.f64 y #s(literal -1/2 binary64)) x)
accuracy	25.251166954483196	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
accuracy	0	(fma.f64 x #s(literal 1/2 binary64) z)
accuracy	19.719187887510397	#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
accuracy	0	(*.f64 y x)
accuracy	43.25649935539626	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
accuracy	0	(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
accuracy	0	(+.f64 #s(literal 1/2 binary64) y)

Samples

29.0ms

256×

valid

Compiler

Compiled 89 to 19 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-add: 6.0ms (35.9% of total)

ival-mult: 6.0ms (35.9% of total)

ival-div: 2.0ms (12% of total)

ival-sub: 2.0ms (12% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.4%)

Memory

-9.3MiB live, 27.5MiB allocated

Counts

11 → 300

Calls

Call 1

Inputs
#s(alt (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z) (patch (fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) y) (patch (+.f64 #s(literal 1/2 binary64) y) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 y x)) (patch #s(approx (+ (+ (/ x 2) ( y x)) z) (*.f64 y x)) #<representation binary64>) () ())
#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/2 binary64) z) (patch (fma.f64 x #s(literal 1/2 binary64) z) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) ( y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 y #s(literal -1/2 binary64)) x) (patch (.f64 (-.f64 y #s(literal -1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 y #s(literal -1/2 binary64)) (patch (-.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (+ (/ x 2) (* y x)) (.f64 y x)) z) (patch (+.f64 #s(approx (+ (/ x 2) ( y x)) (*.f64 y x)) z) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ x 2) (* y x)) (.f64 y x)) (patch #s(approx (+ (/ x 2) ( y x)) (*.f64 y x)) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	((+ (* (+ 1/2 y) x) z) (+ 1/2 y) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms	x	@	-inf	((+ (* (+ 1/2 y) x) z) (+ 1/2 y) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms	x	@	inf	((+ (* (+ 1/2 y) x) z) (+ 1/2 y) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms	y	@	-inf	((+ (* (+ 1/2 y) x) z) (+ 1/2 y) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))
1.0ms	x	@	0	((+ (* (+ 1/2 y) x) z) (+ 1/2 y) (+ (+ (/ x 2) (* y x)) z) (* y x) (+ (+ (/ x 2) (* y x)) z) (+ (* x 1/2) z) (+ (+ (/ x 2) (* y x)) z) (* (- y -1/2) x) (- y -1/2) (+ (+ (/ x 2) (* y x)) z) (+ (/ x 2) (* y x)))

simplify139.0ms (3.2%)

Memory

-2.8MiB live, 125.9MiB allocated

Algorithm

1×	egg-herbie

Rules

6 552×	`lower-fma.f64`
6 552×	`lower-fma.f32`
2 372×	`lower-*.f64`
2 372×	`lower-*.f32`
1 404×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	1552
1	270	1552
2	723	1552
3	2015	1552
4	4164	1552
5	6246	1552
6	7552	1552
0	8054	1394

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 278

Calls

Call 1

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

rewrite250.0ms (5.7%)

Memory

1.0MiB live, 242.4MiB allocated

Rules

9 340×	`lower-fma.f32`
9 336×	`lower-fma.f64`
4 786×	`lower-*.f32`
4 782×	`lower-*.f64`
3 664×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	90
0	30	90
1	136	77
2	1039	77
0	8716	77

Stop Event

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

Counts

11 → 380

Calls

Call 1

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

Outputs
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eval141.0ms (3.2%)

Memory: -0.2MiB live, 109.4MiB allocated
Compiler: Compiled 9 931 to 1 104 computations (88.9% saved)

prune69.0ms (1.6%)

Memory

-6.3MiB live, 40.1MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	685	1	686
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	685	6	691

Accuracy

100.0%

Counts

691 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
✓	71.8%	(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
✓	69.2%	#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
✓	60.5%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
▶	30.3%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
✓	32.4%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

Compiler

Compiled 32 to 37 computations (-15.6% saved)

simplify4.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (- y -1/2) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))

Rules

28×	`lower-+.f64`
28×	`lower-+.f32`
12×	`lower-fma.f64`
12×	`lower-fma.f32`
12×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
0	15	31
1	23	31
2	31	31
3	33	31
0	33	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize66.0ms (1.5%)

Memory

-12.3MiB live, 25.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)
accuracy	25.251166954483196	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
accuracy	28.790500107251944	#s(approx (- y -1/2) #s(literal 1/2 binary64))

Samples

59.0ms

256×

valid

Compiler

Compiled 21 to 14 computations (33.3% saved)

Precisions

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

ival-mult: 3.0ms (33.2% of total)

ival-div: 2.0ms (22.1% of total)

ival-add: 2.0ms (22.1% of total)

ival-sub: 1.0ms (11.1% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs

#s(alt #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())

#s(alt (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x) (patch (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())

#s(alt #s(approx (- y -1/2) #s(literal 1/2 binary64)) (patch #s(approx (- y -1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())

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

Calls

9 calls:

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

simplify135.0ms (3.1%)

Memory

11.2MiB live, 83.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 682×	`lower-fma.f64`
7 682×	`lower-fma.f32`
3 072×	`lower-*.f64`
3 072×	`lower-*.f32`
1 368×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	362
1	189	362
2	515	362
3	1566	362
4	3483	362
5	6324	362
0	8421	334

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 67

Calls

Call 1

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

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

rewrite302.0ms (6.8%)

Memory

-2.5MiB live, 205.9MiB allocated

Rules

7 604×	`lower-fma.f64`
7 604×	`lower-fma.f32`
4 348×	`lower-*.f32`
4 346×	`lower-*.f64`
3 082×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	29
0	15	29
1	71	27
2	561	27
3	6887	27
0	8161	26

Stop Event

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

Counts

3 → 4

Calls

Call 1

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

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

eval6.0ms (0.1%)

Memory: 12.5MiB live, 12.5MiB allocated
Compiler: Compiled 470 to 29 computations (93.8% saved)

prune19.0ms (0.4%)

Memory

-27.4MiB live, 11.5MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	71	6	77

Accuracy

100.0%

Counts

77 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
✓	71.8%	(+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)
✓	69.2%	#s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z))
✓	60.5%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))
✓	30.3%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x))
✓	32.4%	#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

Compiler

Compiled 73 to 60 computations (17.8% saved)

regimes54.0ms (1.2%)

Memory

-8.7MiB live, 30.4MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 19 to 24 computations (-26.3% saved)

regimes13.0ms (0.3%)

Memory

18.2MiB live, 18.2MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
89.6%	3	`x`
99.1%	3	`y`
84.8%	3	`z`
81.4%	3	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
90.3%	4	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`

Compiler

Compiled 19 to 24 computations (-26.3% saved)

regimes7.0ms (0.2%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

4 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
88.6%	3	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
83.9%	3	`x`
88.4%	3	`y`

Compiler

Compiled 9 to 13 computations (-44.4% saved)

regimes4.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
88.2%	3	`y`
80.6%	3	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes94.0ms (2.1%)

Memory

-23.3MiB live, 15.4MiB allocated

Counts

2 → 3

Calls

Call 1

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

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

Calls

5 calls:

87.0ms	z
2.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
2.0ms	y
2.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
2.0ms	x

Results

Accuracy	Segments	Branch
41.7%	3	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
41.7%	3	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
41.0%	3	`x`
36.8%	2	`z`
59.7%	3	`y`

Compiler

Compiled 19 to 24 computations (-26.3% saved)

regimes7.0ms (0.2%)

Memory

12.5MiB live, 12.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

Outputs
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
32.4%	1	`z`
32.4%	1	`x`
32.4%	1	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
32.4%	1	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
32.4%	1	`y`

Compiler

Compiled 19 to 24 computations (-26.3% saved)

bsearch37.0ms (0.8%)

Memory

-11.9MiB live, 28.8MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
21.0ms	0.005637458655620159	3.2867663204374495
14.0ms	-6.838565519232254e+30	-3.3322948949988894e+20

Samples

23.0ms

288×

valid

Compiler

Compiled 210 to 266 computations (-26.7% saved)

Precisions

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

ival-div: 2.0ms (28.8% of total)

ival-add: 2.0ms (28.8% of total)

ival-mult: 2.0ms (28.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.7777979327858898e+53	1.3075801784879614e+60
0.0ms	-2.6286685459136853e+62	-2.1225490596143815e+47

Compiler

Compiled 12 to 14 computations (-16.7% saved)

bsearch20.0ms (0.5%)

Memory

20.8MiB live, 20.8MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
8.0ms	7.39569891487526e+21	7.469222516060913e+22
10.0ms	-1.0070667714625345e+46	-1.2727407837918372e+44

Samples

10.0ms

208×

valid

Compiler

Compiled 129 to 183 computations (-41.9% saved)

Precisions

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

ival-add: 2.0ms (40.7% of total)

ival-div: 1.0ms (20.3% of total)

ival-mult: 1.0ms (20.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.005637458655620159	3.2867663204374495
1.0ms	-6.838565519232254e+30	-3.3322948949988894e+20

Compiler

Compiled 174 to 266 computations (-52.9% saved)

simplify50.0ms (1.1%)

Memory

-1.4MiB live, 36.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative-binary64-+.f64`
8×	`-commutative-binary64-.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`neg-sub0-binary64--.f64-neg.f64`
2×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	230
1	54	230
2	59	230
3	61	230
4	62	230

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
(if (<=.f64 y #s(literal -340000000000000000000 binary64)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (.f64 y x)) z) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)))
(if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) #s(literal -200000000000000007004399371886322346092160635596623651209740288 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) #s(literal 199999999999999998644189734872325595292341688388812800 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(if (<=.f64 y #s(literal -509999999999999973683596904224851633389961216 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 y x)) (if (<=.f64 y #s(literal 41999999999999995805696 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))))
(if (<=.f64 y #s(literal -340000000000000000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 y x)) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #s(approx (+ (+ (/ x 2) ( y x)) z) (*.f64 y x))))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))

Outputs
(fma.f64 (+.f64 #s(literal 1/2 binary64) y) x z)
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(if (<=.f64 y #s(literal -340000000000000000000 binary64)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (.f64 y x)) z) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 y x)) z)))
(if (<=.f64 y #s(literal -340000000000000000000 binary64)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (.f64 x y)) z) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) (+.f64 #s(approx (+ (/ x 2) (* y x)) (*.f64 x y)) z)))
(if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) #s(literal -200000000000000007004399371886322346092160635596623651209740288 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 y x)) #s(literal 199999999999999998644189734872325595292341688388812800 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x y)) #s(literal -200000000000000007004399371886322346092160635596623651209740288 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (.f64 (-.f64 y #s(literal -1/2 binary64)) x)) (if (<=.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (.f64 x y)) #s(literal 199999999999999998644189734872325595292341688388812800 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 (-.f64 y #s(literal -1/2 binary64)) x))))
(if (<=.f64 y #s(literal -509999999999999973683596904224851633389961216 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 y x)) (if (<=.f64 y #s(literal 41999999999999995805696 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))))
(if (<=.f64 y #s(literal -509999999999999973683596904224851633389961216 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 x y)) (if (<=.f64 y #s(literal 41999999999999995805696 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (fma.f64 x #s(literal 1/2 binary64) z)) #s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y))))
(if (<=.f64 y #s(literal -340000000000000000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 y x)) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #s(approx (+ (+ (/ x 2) ( y x)) z) (*.f64 y x))))
(if (<=.f64 y #s(literal -340000000000000000000 binary64)) #s(approx (+ (+ (/ x 2) (* y x)) z) (.f64 x y)) (if (<=.f64 y #s(literal 1/2 binary64)) #s(approx (+ (+ (/ x 2) ( y x)) z) (.f64 #s(approx (- y -1/2) #s(literal 1/2 binary64)) x)) #s(approx (+ (+ (/ x 2) ( y x)) z) (*.f64 x y))))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 y x))
#s(approx (+ (+ (/ x 2) (* y x)) z) (*.f64 x y))

soundness808.0ms (18.3%)

Memory

-14.2MiB live, 424.8MiB allocated

Rules

7 074×	`lower-fma.f64`
7 074×	`lower-fma.f32`
6 552×	`lower-fma.f64`
6 552×	`lower-fma.f32`
6 434×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	1552
1	270	1552
2	723	1552
3	2015	1552
4	4164	1552
5	6246	1552
6	7552	1552
0	8054	1394
0	8	22
0	12	22
1	52	18
2	452	18
3	6077	18
0	8040	17
0	57	440
1	174	440
2	488	440
3	1308	440
4	3609	440
5	6674	440
0	8210	412

Stop Event

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

Compiler

Compiled 169 to 102 computations (39.6% saved)

preprocess45.0ms (1%)

Memory: -11.0MiB live, 102.0MiB allocated
Compiler: Compiled 246 to 98 computations (60.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.1s (24.3%)

explain188.0ms (4.3%)

preprocess422.0ms (9.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize24.0ms (0.6%)

series29.0ms (0.6%)

simplify115.0ms (2.6%)

rewrite164.0ms (3.7%)

eval39.0ms (0.9%)

prune9.0ms (0.2%)

simplify6.0ms (0.1%)

localize43.0ms (1%)

series18.0ms (0.4%)

simplify139.0ms (3.2%)

rewrite250.0ms (5.7%)

eval141.0ms (3.2%)

prune69.0ms (1.6%)

simplify4.0ms (0.1%)

localize66.0ms (1.5%)

series5.0ms (0.1%)

simplify135.0ms (3.1%)

rewrite302.0ms (6.8%)

eval6.0ms (0.1%)

prune19.0ms (0.4%)

regimes54.0ms (1.2%)

regimes13.0ms (0.3%)

regimes7.0ms (0.2%)

regimes4.0ms (0.1%)

regimes94.0ms (2.1%)

regimes7.0ms (0.2%)

bsearch37.0ms (0.8%)

bsearch1.0ms (0%)

bsearch20.0ms (0.5%)

bsearch2.0ms (0.1%)

simplify50.0ms (1.1%)

soundness808.0ms (18.3%)

preprocess45.0ms (1%)

end0.0ms (0%)

Profiling