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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample932.0ms (40.4%)

Memory

16.3MiB live, 1 114.0MiB allocated

Samples

631.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 446.0ms

ival-mult: 314.0ms (70.3% of total)

ival-sub: 117.0ms (26.2% of total)

ival-true: 6.0ms (1.3% of total)

exact: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain124.0ms (5.4%)

Memory

-16.5MiB live, 151.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
4	-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
1	-	-	`(.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	-	-	`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	4	0
↳	`(*.f64 x x)`	overflow	64
↳	`(*.f64 y #s(literal 4 binary64))`	overflow	1
↳	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	overflow	36
`*.f64`	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	5	0
-	0	251

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	0	0	251

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	251
1	5

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

46.0ms

512×

valid

Compiler

Compiled 61 to 28 computations (54.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 12.0ms (77.2% of total)

ival-sub: 2.0ms (12.9% of total)

ival-true: 1.0ms (6.4% of total)

exact: 0.0ms (0% of total)

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

preprocess26.0ms (1.1%)

Memory

0.9MiB live, 37.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	87	84
2	226	84
3	497	81
4	629	81
0	8	9
0	12	9
1	23	9
2	61	9
3	143	9
4	226	9
5	272	9
0	272	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: 0.3MiB live, 0.2MiB 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
▶	98.4%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify6.0ms (0.3%)

Memory

10.2MiB live, 10.2MiB 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	1	(-.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	23	24
2	61	24
3	143	24
4	226	24
5	272	24
0	272	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

localize23.0ms (1%)

Memory

1.7MiB live, 38.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 y #s(literal 4 binary64)) z)
accuracy	0.0	(*.f64 y #s(literal 4 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.9023396216604117	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Samples

18.0ms

256×

valid

Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions

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

ival-mult: 6.0ms (80.2% of total)

ival-sub: 1.0ms (13.4% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.5%)

Memory

-19.6MiB live, 16.3MiB allocated

Counts

4 → 11

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

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	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	x	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))

simplify128.0ms (5.6%)

Memory

18.3MiB live, 221.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	87
1	89	87
2	273	87
3	1359	87
4	4964	87
0	8120	80

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 11

Calls

Call 1

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

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

rewrite128.0ms (5.6%)

Memory

14.5MiB live, 211.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	12	20
1	38	20
2	268	20
3	3015	20
0	8706	19

Stop Event

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

Counts

4 → 371

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
(.f64 (/.f64 (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 2 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 2 binary64))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x)))
(.f64 (/.f64 (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 64 binary64) (pow.f64 (.f64 (.f64 z y) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (/.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 2 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 6 binary64)) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))))) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 2 binary64)))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64))))) (neg.f64 (pow.f64 (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (neg.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))))) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)))) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (neg.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))))) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) #s(literal 2 binary64))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))
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(.f64 (sqrt.f64 y) (sqrt.f64 (.f64 (pow.f64 (*.f64 z #s(literal 4 binary64)) #s(literal 2 binary64)) y)))
(.f64 (exp.f64 (log.f64 (.f64 z y))) (exp.f64 (log.f64 #s(literal 4 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) (exp.f64 (log.f64 (.f64 z y))))
(.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 (.f64 z #s(literal 4 binary64)))))
(.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) y))))
(.f64 (exp.f64 (log.f64 (.f64 z #s(literal 4 binary64)))) (exp.f64 (log.f64 y)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) y))) (exp.f64 (log.f64 z)))
(.f64 (fabs.f64 (.f64 z y)) #s(literal 4 binary64))
(.f64 (fabs.f64 z) (.f64 (fabs.f64 y) #s(literal 4 binary64)))
(.f64 (.f64 (fabs.f64 y) #s(literal 4 binary64)) (fabs.f64 z))
(.f64 (.f64 (fabs.f64 z) #s(literal 4 binary64)) (fabs.f64 y))
(.f64 (fabs.f64 y) (fabs.f64 (.f64 #s(literal -4 binary64) z)))
(.f64 (fabs.f64 y) (.f64 (fabs.f64 z) #s(literal 4 binary64)))
(.f64 (.f64 z y) #s(literal 4 binary64))
(.f64 (.f64 z #s(literal 4 binary64)) y)
(.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (.f64 z y) (.f64 z (*.f64 #s(literal 4 binary64) y)))))
(.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 y (.f64 (.f64 z (*.f64 #s(literal 4 binary64) y)) z))))
(.f64 z (.f64 #s(literal 4 binary64) y))
(.f64 (.f64 #s(literal 4 binary64) y) z)
(.f64 #s(literal 4 binary64) (fabs.f64 (fabs.f64 (.f64 z y))))
(.f64 #s(literal 4 binary64) (fabs.f64 (.f64 (neg.f64 y) z)))
(.f64 #s(literal 4 binary64) (fabs.f64 (.f64 z y)))
(.f64 #s(literal 4 binary64) (.f64 z y))
(.f64 y (.f64 z #s(literal 4 binary64)))
(pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 1 binary64))
(pow.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 1 binary64))
(neg.f64 (.f64 (.f64 #s(literal -4 binary64) y) z))
(sqrt.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)))
(fabs.f64 (.f64 (.f64 #s(literal -4 binary64) y) z))
(fabs.f64 (.f64 z (.f64 #s(literal 4 binary64) y)))
(exp.f64 (/.f64 (log.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 z (*.f64 #s(literal 4 binary64) y))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (.f64 z (.f64 #s(literal 4 binary64) y))))
(+.f64 (cosh.f64 (log.f64 (.f64 z (.f64 #s(literal 4 binary64) y)))) (sinh.f64 (log.f64 (.f64 z (.f64 #s(literal 4 binary64) y)))))
(*.f64 (neg.f64 (neg.f64 y)) #s(literal 4 binary64))
(*.f64 #s(literal -4 binary64) (neg.f64 y))
(*.f64 (neg.f64 y) #s(literal -4 binary64))
(*.f64 #s(literal 4 binary64) (neg.f64 (neg.f64 y)))
(*.f64 #s(literal 4 binary64) y)
(*.f64 y #s(literal 4 binary64))
(neg.f64 (*.f64 #s(literal -4 binary64) y))

eval91.0ms (4%)

Memory: -16.7MiB live, 118.6MiB allocated
Compiler: Compiled 11 620 to 835 computations (92.8% saved)

prune19.0ms (0.8%)

Memory

-15.5MiB live, 23.3MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	375	3	378
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	376	3	379

Accuracy

100.0%

Counts

379 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))
▶	99.2%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
▶	51.2%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify7.0ms (0.3%)

Memory

12.8MiB live, 12.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	64
0	24	64
1	47	63
2	105	63
3	188	63
4	288	63
0	288	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (1.7%)

Memory

-5.8MiB live, 69.8MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 #s(literal -4 binary64) y)
accuracy	0.5039007452111204	(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))
accuracy	0.0	(.f64 (.f64 #s(literal -4 binary64) y) z)
accuracy	0.0	(*.f64 #s(literal -4 binary64) y)
accuracy	0.49999449521112044	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
accuracy	0.0	(*.f64 z y)
accuracy	0.00390625	(.f64 (.f64 z y) #s(literal -4 binary64))
accuracy	31.234553682510715	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Samples

30.0ms

256×

valid

Compiler

Compiled 62 to 17 computations (72.6% saved)

Precisions

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

ival-mult: 14.0ms (80.4% of total)

ival-add: 2.0ms (11.5% of total)

ival-sub: 1.0ms (5.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.3%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

8 → 15

Calls

Call 1

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

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

Calls

9 calls:

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

simplify117.0ms (5.1%)

Memory

-20.8MiB live, 135.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	113
1	127	113
2	406	113
3	1591	113
4	5241	113
0	8107	102

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 15

Calls

Call 1

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

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

rewrite181.0ms (7.9%)

Memory

0.3MiB live, 236.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	50
0	24	50
1	80	49
2	600	49
3	6926	49
0	8041	49

Stop Event

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

Counts

8 → 425

Calls

Call 1

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

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z))
(.f64 (.f64 (neg.f64 z) (neg.f64 y)) #s(literal -4 binary64))
(.f64 (.f64 (neg.f64 z) #s(literal -4 binary64)) (neg.f64 y))
(.f64 (.f64 (neg.f64 z) #s(literal 4 binary64)) y)
(.f64 (neg.f64 (.f64 z #s(literal 4 binary64))) y)
(.f64 (.f64 #s(literal -4 binary64) z) y)
(.f64 (neg.f64 y) (.f64 z #s(literal 4 binary64)))
(.f64 (.f64 (neg.f64 z) y) #s(literal 4 binary64))
(.f64 (neg.f64 z) (.f64 #s(literal 4 binary64) y))
(.f64 (.f64 z #s(literal 4 binary64)) (neg.f64 y))
(.f64 (.f64 #s(literal -4 binary64) y) z)
(.f64 #s(literal -4 binary64) (.f64 z y))
(.f64 (.f64 z y) #s(literal -4 binary64))
(.f64 z (.f64 #s(literal -4 binary64) y))
(.f64 (.f64 #s(literal 4 binary64) y) (neg.f64 z))
(.f64 #s(literal 4 binary64) (.f64 (neg.f64 z) y))
(.f64 y (neg.f64 (.f64 z #s(literal 4 binary64))))
(.f64 y (.f64 #s(literal -4 binary64) z))
(neg.f64 (.f64 z (.f64 #s(literal 4 binary64) y)))
(*.f64 z y)
(*.f64 y z)
(.f64 (/.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) #s(literal 2 binary64)))) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 6 binary64)))) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x)))
(.f64 (/.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (/.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x))))
(.f64 (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) (.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))))) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))
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(fma.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 #s(literal -4 binary64) y) (/.f64 (.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) z) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(fma.f64 (.f64 #s(literal -4 binary64) y) (neg.f64 z) (.f64 x x))
(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 (neg.f64 x) x))
(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))
(fma.f64 #s(literal -4 binary64) (/.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal -4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(fma.f64 #s(literal -4 binary64) (.f64 (neg.f64 z) y) (.f64 x x))
(fma.f64 #s(literal -4 binary64) (.f64 z y) (.f64 (neg.f64 x) x))
(fma.f64 #s(literal -4 binary64) (.f64 z y) (.f64 x x))
(fma.f64 (.f64 z y) (/.f64 (.f64 #s(literal 16 binary64) (.f64 z y)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x))))
(fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 (neg.f64 x) x))
(fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x))
(fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))
(fma.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (/.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(fma.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 z (/.f64 (.f64 (.f64 #s(literal 16 binary64) (.f64 z y)) y) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x))))
(fma.f64 z (.f64 #s(literal -4 binary64) y) (.f64 (neg.f64 x) x))
(fma.f64 z (.f64 #s(literal -4 binary64) y) (.f64 x x))
(fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))
(fma.f64 (.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) z) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(fma.f64 (.f64 #s(literal 4 binary64) y) (neg.f64 z) (.f64 (neg.f64 x) x))
(fma.f64 (.f64 #s(literal 4 binary64) y) (neg.f64 z) (.f64 x x))
(fma.f64 (.f64 #s(literal 4 binary64) y) z (.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 (neg.f64 z) y) (.f64 (neg.f64 x) x))
(fma.f64 #s(literal 4 binary64) (.f64 (neg.f64 z) y) (.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 z y) (.f64 x x))
(fma.f64 y (/.f64 (.f64 (pow.f64 (.f64 z #s(literal 4 binary64)) #s(literal 2 binary64)) y) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(fma.f64 y (neg.f64 (.f64 #s(literal -4 binary64) z)) (.f64 x x))
(fma.f64 y (neg.f64 (.f64 z #s(literal 4 binary64))) (.f64 (neg.f64 x) x))
(fma.f64 y (neg.f64 (.f64 z #s(literal 4 binary64))) (.f64 x x))
(fma.f64 y (.f64 #s(literal -4 binary64) z) (.f64 (neg.f64 x) x))
(fma.f64 y (.f64 #s(literal -4 binary64) z) (.f64 x x))
(fma.f64 y (.f64 z #s(literal 4 binary64)) (.f64 x x))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))))
(fma.f64 x (neg.f64 x) (.f64 (.f64 #s(literal -4 binary64) y) z))
(fma.f64 x x (.f64 (neg.f64 (neg.f64 z)) (.f64 #s(literal 4 binary64) y)))
(fma.f64 x x (.f64 (neg.f64 (neg.f64 y)) (.f64 z #s(literal 4 binary64))))
(fma.f64 x x (.f64 (neg.f64 (.f64 (neg.f64 z) y)) #s(literal -4 binary64)))
(fma.f64 x x (.f64 (neg.f64 (neg.f64 z)) (.f64 #s(literal -4 binary64) y)))
(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
(fma.f64 x x (.f64 z (.f64 #s(literal 4 binary64) y)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))))
(-.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(-.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 z)) (*.f64 #s(literal 4 binary64) y)))
(-.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 y)) (*.f64 z #s(literal 4 binary64))))
(-.f64 (.f64 x x) (.f64 (neg.f64 (*.f64 (neg.f64 z) y)) #s(literal -4 binary64)))
(-.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 z)) (*.f64 #s(literal -4 binary64) y)))
(-.f64 (.f64 x x) (.f64 (*.f64 #s(literal -4 binary64) y) z))
(-.f64 (.f64 x x) (.f64 z (*.f64 #s(literal 4 binary64) y)))
(-.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (*.f64 (neg.f64 x) x))
(-.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (*.f64 x x))
(-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))) (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))))
(+.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))))
(+.f64 (.f64 (neg.f64 x) x) (.f64 (*.f64 #s(literal -4 binary64) y) z))
(+.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 z)) (*.f64 #s(literal 4 binary64) y)))
(+.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 y)) (*.f64 z #s(literal 4 binary64))))
(+.f64 (.f64 x x) (.f64 (neg.f64 (*.f64 (neg.f64 z) y)) #s(literal -4 binary64)))
(+.f64 (.f64 x x) (.f64 (neg.f64 (neg.f64 z)) (*.f64 #s(literal -4 binary64) y)))
(+.f64 (.f64 x x) (.f64 (*.f64 #s(literal -4 binary64) y) z))
(+.f64 (.f64 x x) (.f64 z (*.f64 #s(literal 4 binary64) y)))
(+.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (*.f64 (neg.f64 x) x))
(+.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (*.f64 x x))
(+.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval30.0ms (1.3%)

Memory: 14.8MiB live, 51.1MiB allocated
Compiler: Compiled 6 213 to 510 computations (91.8% saved)

prune14.0ms (0.6%)

Memory

-13.6MiB live, 24.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	240	3	243

Accuracy

100.0%

Counts

243 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))
✓	99.2%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
✓	51.2%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Compiler

Compiled 71 to 47 computations (33.8% saved)

regimes13.0ms (0.6%)

Memory

28.1MiB live, 28.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

7 calls:

2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	y
2.0ms	z
2.0ms	x
2.0ms	(-.f64 (.f64 x x) (.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 (0.6%)

Memory

-36.4MiB live, 18.5MiB 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 (.f64 z y) #s(literal -4 binary64)))

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

Calls

7 calls:

6.0ms	(*.f64 x x)
1.0ms	y
1.0ms	(*.f64 y #s(literal 4 binary64))
1.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
1.0ms	x

Results

Accuracy	Segments	Branch
51.2%	1	`x`
51.2%	1	`y`
51.2%	1	`z`
51.2%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
51.2%	1	`(*.f64 x x)`
51.2%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
51.2%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

simplify11.0ms (0.5%)

Memory

16.3MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	26	23
2	63	23
3	147	23
4	238	23
5	283	23

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness346.0ms (15%)

Memory

-10.6MiB live, 145.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	12	20
1	38	20
2	268	20
3	3015	20
0	8706	19
0	36	87
1	89	87
2	273	87
3	1359	87
4	4964	87
0	8120	80

Stop Event

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

Compiler

Compiled 45 to 33 computations (26.7% saved)

preprocess41.0ms (1.8%)

Memory: -3.7MiB live, 73.0MiB allocated
Remove: (abs x)
Compiler: Compiled 112 to 88 computations (21.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	30	88
1	87	84
2	226	84
3	497	81
4	629	81
0	8	9
0	12	9
1	23	9
2	61	9
3	143	9
4	226	9
5	272	9
0	272	8

Iter	Nodes	Cost
0	30	88
1	87	84
2	226	84
3	497	81
4	629	81
0	8	9
0	12	9
1	23	9
2	61	9
3	143	9
4	226	9
5	272	9
0	272	8

start0.0ms (0%)

analyze0.0ms (0%)

sample932.0ms (40.4%)

explain124.0ms (5.4%)

preprocess26.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.3%)

localize23.0ms (1%)

series11.0ms (0.5%)

simplify128.0ms (5.6%)

rewrite128.0ms (5.6%)

eval91.0ms (4%)

prune19.0ms (0.8%)

simplify7.0ms (0.3%)

localize38.0ms (1.7%)

series7.0ms (0.3%)

simplify117.0ms (5.1%)

rewrite181.0ms (7.9%)

eval30.0ms (1.3%)

prune14.0ms (0.6%)

regimes13.0ms (0.6%)

regimes13.0ms (0.6%)

simplify11.0ms (0.5%)

soundness346.0ms (15%)

preprocess41.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	30	88
1	87	84
2	226	84
3	497	81
4	629	81
0	8	9
0	12	9
1	23	9
2	61	9
3	143	9
4	226	9
5	272	9
0	272	8