Metrics for Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB 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)

sample676.0ms (15.1%)

Memory

37.1MiB live, 1 298.3MiB allocated

Samples

423.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 230.0ms

ival-mult: 174.0ms (75.7% of total)

ival-sub: 41.0ms (17.8% of total)

ival-true: 6.0ms (2.6% of total)

exact: 6.0ms (2.6% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain126.0ms (2.8%)

Memory

-33.7MiB live, 164.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
3	-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
0	-	-	`y`
0	-	-	`(*.f64 y #s(literal 4 binary64))`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`z`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`	nan-rescue	3	0
↳	`(*.f64 x x)`	overflow	72
↳	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	overflow	48

Confusion

	Predicted +	Predicted -
+	3	0
-	0	253

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	0	0	253

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	253
1	3

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

72.0ms

512×

valid

Compiler

Compiled 85 to 36 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 9.0ms (69% of total)

ival-sub: 3.0ms (23% of total)

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

exact: 0.0ms (0% of total)

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

preprocess50.0ms (1.1%)

Memory

12.9MiB live, 49.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	99	84
2	255	81
3	609	81
4	908	81
5	1035	81
6	1075	81
7	1075	81
0	8	9
0	12	9
1	21	9
2	51	9
3	101	9
4	136	9
5	178	9
6	238	9
7	296	9
8	391	9
9	445	9
10	475	9
0	475	8

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

(sort y z)

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

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify14.0ms (0.3%)

Memory

11.8MiB live, 11.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y #s(literal 4 binary64))
cost-diff	0	(.f64 (.f64 y #s(literal 4 binary64)) z)
cost-diff	0	(*.f64 x x)
cost-diff	128	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	296	24
8	391	24
9	445	24
10	475	24
0	475	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize33.0ms (0.7%)

Memory

-14.2MiB live, 22.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 (.f64 y #s(literal 4 binary64)) z)
accuracy	0	(*.f64 y #s(literal 4 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.6640604358302059	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Samples

28.0ms

256×

valid

Compiler

Compiled 50 to 18 computations (64% saved)

Precisions

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

ival-mult: 4.0ms (63.7% of total)

ival-sub: 1.0ms (15.9% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

9.6MiB live, 9.6MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (pow x 2) (taylor 0 z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor 0 y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor 0 y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) (* 4 z))) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) (* 4 z))) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (pow x 2) y) (* 4 z))) (taylor inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z)))) (taylor -inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z)))) (taylor -inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z)))) (taylor -inf y) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 (* y z)) (taylor -inf y) (#s(alt (.f64 (.f64 y #s(literal 4 binary64)) z) (patch (.f64 (.f64 y #s(literal 4 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 y) (taylor -inf y) (#s(alt (.f64 y #s(literal 4 binary64)) (patch (.f64 y #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) (* 4 (* y z))) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) (* 4 (* y z))) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) (* 4 (* y z))) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) (patch (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	y	@	0	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	z	@	0	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	y	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))

simplify118.0ms (2.6%)

Memory

-4.7MiB live, 108.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	472
1	96	472
2	258	472
3	1041	472
4	3039	472
5	5802	472
6	7660	472
0	8001	445

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* -4 (* y z))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* -4 (* y z))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (* y z))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (* y z))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* y (- (/ (pow x 2) y) (* 4 z)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* y (- (/ (pow x 2) y) (* 4 z)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* y (- (/ (pow x 2) y) (* 4 z)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 (* y z))
(.f64 #s(literal 4 binary64) (.f64 z y))
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* 4 y)
(*.f64 #s(literal 4 binary64) y)
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(- (pow x 2) (* 4 (* y z)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(- (pow x 2) (* 4 (* y z)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(- (pow x 2) (* 4 (* y z)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite229.0ms (5.1%)

Memory

13.5MiB live, 300.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	12	20
1	36	20
2	242	20
3	2285	20
0	8408	19

Stop Event

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

Counts

4 → 199

Calls

Call 1

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

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

eval32.0ms (0.7%)

Memory: -6.1MiB live, 67.7MiB allocated
Compiler: Compiled 8 834 to 624 computations (92.9% saved)

prune6.0ms (0.1%)

Memory

20.1MiB live, 20.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	279	4	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	280	4	284

Accuracy

100.0%

Counts

284 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
▶	99.2%	(fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64)))
▶	52.6%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))
▶	54.8%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 26 to 26 computations (0% saved)

simplify20.0ms (0.4%)

Memory

-29.0MiB live, 17.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	81
0	24	81
1	41	79
2	66	79
3	105	79
4	141	79
5	183	79
6	243	79
7	304	79
8	399	79
9	453	79
10	483	79
0	483	79

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (0.9%)

Memory

14.5MiB live, 89.6MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 #s(literal -4 binary64) z)
accuracy	0.2539034976055602	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
accuracy	0	(*.f64 z y)
accuracy	0.0078125	(.f64 (.f64 z y) #s(literal -4 binary64))
accuracy	0.5117132452111204	(fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64)))
accuracy	0	(*.f64 z y)
accuracy	0.0078125	(.f64 (.f64 z y) #s(literal -4 binary64))
accuracy	30.31608855471714	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))
accuracy	0	(*.f64 x x)
accuracy	28.949913815020356	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Samples

31.0ms

256×

valid

Compiler

Compiled 138 to 29 computations (79% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 10.0ms (56.3% of total)

ival-add: 6.0ms (33.8% of total)

ival-sub: 1.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

8 → 216

Calls

Call 1

Inputs
#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())
#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor 0 z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -4 (* y z)) (pow x 2)) (taylor 0 z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor 0 z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (- (/ (pow x 2) z) (* 4 y))) (taylor inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -4 y) (/ (pow x 2) z))) (taylor inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -4 y) (/ (pow x 2) z))) (taylor inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -4 y) (/ (pow x 2) z))) (taylor inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -4 y) (/ (pow x 2) z))) (taylor inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -4 y) (/ (pow x 2) z))) (taylor inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -4 y) (/ (pow x 2) z))) (taylor inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y)))) (taylor -inf z) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (.f64 (.f64 z y) #s(literal -4 binary64)) (patch (.f64 (.f64 z y) #s(literal -4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor -inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor -inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor -inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y z) (taylor -inf z) (#s(alt (.f64 z y) (patch (.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y)))) (taylor -inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y)))) (taylor -inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y)))) (taylor -inf z) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -4 (* y z)) (taylor -inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y)))) (taylor -inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y)))) (taylor -inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y)))) (taylor -inf z) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor -inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor -inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor -inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (* -4 z) (taylor -inf z) (#s(alt (.f64 #s(literal -4 binary64) z) (patch (.f64 #s(literal -4 binary64) z) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
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#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 x x)) (patch #s(approx (- ( x x) (* (* y 4) z)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) (patch #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) (patch (fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (patch (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* x x) (* (* z y) -4)) (+ (* (* -4 z) y) (* x x)) (* -4 z))
1.0ms	z	@	0	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* x x) (* (* z y) -4)) (+ (* (* -4 z) y) (* x x)) (* -4 z))
1.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* x x) (* (* z y) -4)) (+ (* (* -4 z) y) (* x x)) (* -4 z))
1.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* x x) (* (* z y) -4)) (+ (* (* -4 z) y) (* x x)) (* -4 z))
1.0ms	y	@	0	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* x x) (* (* z y) -4)) (+ (* (* -4 z) y) (* x x)) (* -4 z))

simplify115.0ms (2.6%)

Memory

-4.5MiB live, 113.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	1384
1	134	1384
2	365	1384
3	1179	1384
4	3308	1384
5	6680	1384
0	8143	1276

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 (* y z))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -4 (* y z))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* -4 (* y z))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 (* y z))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -4 (* y z))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -4 (* y z))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -4 z)
(* -4 z)
(* -4 z)
(* -4 z)
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -4 (* y z))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* -4 (* y z))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* -4 (* y z))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -4 (* y z))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* -4 (* y z))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -4 (* y z))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(* -4 (* y z))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))

Outputs
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(* y z)
(*.f64 z y)
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 z)
(*.f64 z #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
(* -4 (* y z))
(.f64 (.f64 z y) #s(literal -4 binary64))
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(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
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(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))
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(fma.f64 (.f64 y #s(literal -4 binary64)) z (.f64 x x))

rewrite276.0ms (6.2%)

Memory

10.4MiB live, 163.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	58
0	24	58
1	81	56
2	542	56
3	6846	56
0	8066	56

Stop Event

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

Counts

8 → 433

Calls

Call 1

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

Outputs
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eval169.0ms (3.8%)

Memory: -39.2MiB live, 175.9MiB allocated
Compiler: Compiled 13 861 to 576 computations (95.8% saved)

prune24.0ms (0.5%)

Memory

32.2MiB live, 69.7MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	739	0	739
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	739	4	743

Accuracy

100.0%

Counts

743 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
✓	99.2%	(fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64)))
✓	52.6%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))
✓	54.8%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 61 to 42 computations (31.1% saved)

regimes23.0ms (0.5%)

Memory

-10.0MiB live, 40.1MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

7 calls:

8.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	x
2.0ms	y
2.0ms	z
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`z`
99.6%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
99.6%	1	`(*.f64 x x)`
99.6%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
99.6%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes17.0ms (0.4%)

Memory

6.6MiB live, 41.4MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

7 calls:

5.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	y
2.0ms	z
2.0ms	x
2.0ms	(.f64 (.f64 y #s(literal 4 binary64)) z)

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`y`
99.2%	1	`z`
99.2%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
99.2%	1	`(*.f64 x x)`
99.2%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
99.2%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes13.0ms (0.3%)

Memory

-1.7MiB live, 36.7MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
82.1%	2	`x`
71.9%	3	`y`
68.6%	3	`z`
77.3%	2	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
82.1%	2	`(*.f64 x x)`
72.5%	3	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
71.9%	3	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes11.0ms (0.3%)

Memory

-1.1MiB live, 36.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Calls

7 calls:

3.0ms	x
1.0ms	z
1.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
1.0ms	(*.f64 y #s(literal 4 binary64))
1.0ms	y

Results

Accuracy	Segments	Branch
54.8%	1	`z`
54.8%	1	`y`
54.8%	1	`(*.f64 y #s(literal 4 binary64))`
54.8%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
54.8%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
54.8%	1	`x`
54.8%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

bsearch15.0ms (0.3%)

Memory

-25.2MiB live, 22.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.0775712310472205e-104	4.588777800900887e-100

Samples

6.0ms

128×

valid

Compiler

Compiled 76 to 118 computations (-55.3% saved)

Precisions

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

ival-mult: 2.0ms (75.7% of total)

ival-sub: 1.0ms (37.9% of total)

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

exact: 0.0ms (0% of total)

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

simplify48.0ms (1.1%)

Memory

6.9MiB live, 44.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	63
1	23	63

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
(fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 5547802472452343/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224 binary64)) #s(approx (- ( x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Outputs
(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
(fma.f64 x x (.f64 (.f64 z y) #s(literal -4 binary64)))
(fma.f64 x x (.f64 (.f64 y z) #s(literal -4 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 5547802472452343/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224 binary64)) #s(approx (- ( x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64))) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))
(if (<=.f64 (.f64 x x) #s(literal 5547802472452343/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224 binary64)) #s(approx (- ( x x) (* (* y 4) z)) (.f64 (.f64 y z) #s(literal -4 binary64))) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

soundness1.4s (31.7%)

Memory

-2.0MiB live, 225.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	472
1	96	472
2	258	472
3	1041	472
4	3039	472
5	5802	472
6	7660	472
0	8001	445
0	8	20
0	12	20
1	36	20
2	242	20
3	2285	20
0	8408	19

Stop Event

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

Compiler

Compiled 81 to 52 computations (35.8% saved)

preprocess973.0ms (21.8%)

Memory

-4.4MiB live, 132.5MiB allocated

Remove

(sort y z)

(abs x)

Compiler

Compiled 186 to 130 computations (30.1% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	296	24
8	391	24
9	445	24
10	475	24
0	475	23

Iter	Nodes	Cost
0	17	81
0	24	81
1	41	79
2	66	79
3	105	79
4	141	79
5	183	79
6	243	79
7	304	79
8	399	79
9	453	79
10	483	79
0	483	79

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	296	24
8	391	24
9	445	24
10	475	24
0	475	23

Iter	Nodes	Cost
0	17	81
0	24	81
1	41	79
2	66	79
3	105	79
4	141	79
5	183	79
6	243	79
7	304	79
8	399	79
9	453	79
10	483	79
0	483	79

start0.0ms (0%)

analyze0.0ms (0%)

sample676.0ms (15.1%)

explain126.0ms (2.8%)

preprocess50.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify14.0ms (0.3%)

localize33.0ms (0.7%)

series9.0ms (0.2%)

simplify118.0ms (2.6%)

rewrite229.0ms (5.1%)

eval32.0ms (0.7%)

prune6.0ms (0.1%)

simplify20.0ms (0.4%)

localize41.0ms (0.9%)

series11.0ms (0.2%)

simplify115.0ms (2.6%)

rewrite276.0ms (6.2%)

eval169.0ms (3.8%)

prune24.0ms (0.5%)

regimes23.0ms (0.5%)

regimes17.0ms (0.4%)

regimes13.0ms (0.3%)

regimes11.0ms (0.3%)

bsearch15.0ms (0.3%)

simplify48.0ms (1.1%)

soundness1.4s (31.7%)

preprocess973.0ms (21.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	296	24
8	391	24
9	445	24
10	475	24
0	475	23

Iter	Nodes	Cost
0	17	81
0	24	81
1	41	79
2	66	79
3	105	79
4	141	79
5	183	79
6	243	79
7	304	79
8	399	79
9	453	79
10	483	79
0	483	79