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

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.0s (15.1%)

Memory

25.5MiB live, 1 153.0MiB allocated

Samples

704.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 279.0ms

ival-mult: 230.0ms (82.4% of total)

ival-sub: 35.0ms (12.5% of total)

ival-true: 6.0ms (2.2% of total)

exact: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain164.0ms (2.5%)

Memory

-8.4MiB live, 244.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(-.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	2	0
↳	`(*.f64 x x)`	overflow	70
↳	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	overflow	35

Confusion

	Predicted +	Predicted -
+	2	0
-	0	254

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	0	0	254

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	254
1	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms

512×

valid

Compiler

Compiled 61 to 28 computations (54.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 30.0ms (90.4% of total)

ival-sub: 2.0ms (6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess28.0ms (0.4%)

Memory

1.5MiB live, 47.5MiB 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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify6.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB 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

localize25.0ms (0.4%)

Memory

-17.5MiB live, 29.4MiB 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	0.4570291858302058	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Samples

19.0ms

256×

valid

Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sub: 6.0ms (55.9% of total)

ival-mult: 5.0ms (46.6% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB 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
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	y	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	x	@	0	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))

simplify131.0ms (2%)

Memory

-3.0MiB live, 183.8MiB 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)

rewrite211.0ms (3.2%)

Memory

1.0MiB live, 384.7MiB 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))

eval78.0ms (1.2%)

Memory: -22.9MiB live, 123.7MiB allocated
Compiler: Compiled 11 620 to 835 computations (92.8% saved)

prune7.0ms (0.1%)

Memory

30.0MiB live, 30.0MiB 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
▶	99.6%	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
▶	99.6%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
▶	51.9%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify10.0ms (0.1%)

Memory

-28.4MiB live, 17.6MiB 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 z #s(literal -4 binary64))
cost-diff	0	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.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	18	64
0	27	64
1	55	63
2	112	63
3	186	63
4	265	63
0	265	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 z #s(literal -4 binary64)) y (.f64 x x))
(*.f64 z #s(literal -4 binary64))
z
#s(literal -4 binary64)
y
(*.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 z #s(literal -4 binary64)) y (.f64 x x))
(fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x))
(*.f64 z #s(literal -4 binary64))
(*.f64 #s(literal -4 binary64) z)
z
#s(literal -4 binary64)
y
(*.f64 x x)
x

localize45.0ms (0.7%)

Memory

9.5MiB live, 108.0MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 z #s(literal -4 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.2578097476055602	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
accuracy	0.0	(.f64 (.f64 #s(literal -4 binary64) y) z)
accuracy	0.0	(*.f64 #s(literal -4 binary64) y)
accuracy	0.24999724760556022	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
accuracy	0.0	(*.f64 z y)
accuracy	0.012382519536884034	(.f64 (.f64 z y) #s(literal -4 binary64))
accuracy	30.758409526305964	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Samples

32.0ms

256×

valid

Compiler

Compiled 62 to 19 computations (69.4% saved)

Precisions

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

ival-mult: 14.0ms (79.4% of total)

ival-add: 2.0ms (11.3% 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)

series8.0ms (0.1%)

Memory

23.1MiB live, 23.1MiB allocated

Counts

9 → 16

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 z #s(literal -4 binary64)) y (.f64 x x))
(*.f64 z #s(literal -4 binary64))
(*.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))))
(* -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	z	@	-inf	((- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* x x) (* (* -4 y) z)) (* (* -4 y) z) (* -4 y) (+ (* (* z -4) y) (* x x)) (* z -4) (* 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) (+ (* (* z -4) y) (* x x)) (* z -4) (* 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) (+ (* (* z -4) y) (* x x)) (* z -4) (* 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) (+ (* (* z -4) y) (* x x)) (* z -4) (* 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) (+ (* (* z -4) y) (* x x)) (* z -4) (* x x))

simplify3.0s (45.3%)

Memory

-292.8MiB live, 214.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	116
1	127	116
2	406	116
3	1591	116
4	5241	116
0	8107	105

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 16

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

rewrite246.0ms (3.7%)

Memory

0.9MiB live, 192.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	53
0	27	53
1	95	52
2	637	52
3	7204	52
0	8017	52

Stop Event

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

Counts

9 → 435

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 z #s(literal -4 binary64)) y (.f64 x x))
(*.f64 z #s(literal -4 binary64))
(*.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)) y)
(.f64 (neg.f64 (.f64 z #s(literal 4 binary64))) y)
(.f64 (.f64 (neg.f64 z) y) #s(literal 4 binary64))
(.f64 (neg.f64 z) (.f64 #s(literal 4 binary64) y))
(.f64 (neg.f64 y) (.f64 z #s(literal 4 binary64)))
(.f64 (.f64 z #s(literal 4 binary64)) (neg.f64 y))
(.f64 (.f64 #s(literal -4 binary64) z) 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 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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.f64 x x))) (pow.f64 x #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) z) 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))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)))) #s(literal 2 binary64)))) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) 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))) (+.f64 (pow.f64 (.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)))) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.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) z) y (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (/.f64 (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.f64 x x))))
(.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.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) z) y (.f64 x x)))))) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x)))
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(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (.f64 x x) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (neg.f64 x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.f64 x x)))))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (neg.f64 z)) (.f64 #s(literal 4 binary64) y)))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (neg.f64 y)) (.f64 z #s(literal 4 binary64))))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (.f64 (neg.f64 z) y)) #s(literal -4 binary64)))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (neg.f64 z)) (.f64 #s(literal -4 binary64) y)))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (neg.f64 y)) (.f64 #s(literal -4 binary64) z)))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (.f64 #s(literal -4 binary64) y) z))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 z (.f64 #s(literal 4 binary64) y)))
(fma.f64 (neg.f64 x) x (.f64 (.f64 #s(literal -4 binary64) y) z))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.f64 x x)))))
(fma.f64 (.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 #s(literal -4 binary64) z) (/.f64 (.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) y) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))))
(fma.f64 (.f64 #s(literal -4 binary64) z) (neg.f64 y) (.f64 x x))
(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 (neg.f64 x) x))
(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
(fma.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (/.f64 (.f64 (.f64 #s(literal -4 binary64) y) z) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))))
(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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.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) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 (.f64 #s(literal 16 binary64) (.f64 z y)) z) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (*.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 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 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.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 (neg.f64 (neg.f64 y)) (.f64 #s(literal -4 binary64) z)))
(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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.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) z) y (.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) z) y (.f64 x x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 (neg.f64 (neg.f64 y)) (*.f64 #s(literal -4 binary64) z)))
(-.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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) z) y (.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) z) y (.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) z) y (.f64 x x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -4 binary64) z) y (.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 (neg.f64 (neg.f64 y)) (*.f64 #s(literal -4 binary64) z)))
(+.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 #s(literal -4 binary64) z)
(*.f64 z #s(literal -4 binary64))
(*.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 (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))))

eval29.0ms (0.4%)

Memory: 10.6MiB live, 54.2MiB allocated
Compiler: Compiled 6 355 to 512 computations (91.9% saved)

prune9.0ms (0.1%)

Memory

27.4MiB live, 27.4MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	238	3	241

Accuracy

100.0%

Counts

241 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
✓	99.6%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
▶	51.9%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) z) y))

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify13.0ms (0.2%)

Memory

-32.0MiB live, 13.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
0	14	26
1	29	26
2	69	26
3	145	26
4	225	26
5	247	26
0	247	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (0.6%)

Memory

-12.3MiB live, 40.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 #s(literal -4 binary64) z) y)
accuracy	0.0	(*.f64 #s(literal -4 binary64) z)
accuracy	30.758409526305964	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) z) y))

Samples

16.0ms

256×

valid

Compiler

Compiled 22 to 13 computations (40.9% saved)

Precisions

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

ival-mult: 7.0ms (78.5% of total)

ival-sub: 1.0ms (11.2% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

3 → 10

Calls

Call 1

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

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))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -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
1.0ms	z	@	-inf	((- (* x x) (* (* y 4) z)) (* (* -4 z) y) (* -4 z))
1.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* (* -4 z) y) (* -4 z))
1.0ms	z	@	0	((- (* x x) (* (* y 4) z)) (* (* -4 z) y) (* -4 z))
0.0ms	y	@	inf	((- (* x x) (* (* y 4) z)) (* (* -4 z) y) (* -4 z))
0.0ms	y	@	0	((- (* x x) (* (* y 4) z)) (* (* -4 z) y) (* -4 z))

simplify127.0ms (1.9%)

Memory

18.5MiB live, 148.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	82
1	89	82
2	273	82
3	1357	82
4	4981	82
0	8137	75

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 10

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

rewrite138.0ms (2.1%)

Memory

15.9MiB live, 209.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
0	14	23
1	44	23
2	276	23
3	3035	23
0	8825	22

Stop Event

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

Counts

3 → 23

Calls

Call 1

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

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

eval3.0ms (0%)

Memory: 7.7MiB live, 7.7MiB allocated
Compiler: Compiled 464 to 84 computations (81.9% saved)

prune29.0ms (0.4%)

Memory

-44.3MiB live, 9.9MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	29	3	32

Accuracy

100.0%

Counts

32 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
✓	51.9%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) z) y))
▶	53.2%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 36 to 29 computations (19.4% saved)

simplify23.0ms (0.4%)

Memory

8.4MiB live, 52.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
0	11	17
1	22	17
2	60	17
3	142	17
4	225	17
5	271	17
0	271	16

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

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

localize19.0ms (0.3%)

Memory

28.2MiB live, 72.5MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	29.976144505786944	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 15 to 10 computations (33.3% saved)

Precisions

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

ival-mult: 5.0ms (80.6% of total)

ival-sub: 1.0ms (16.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

2 → 9

Calls

Call 1

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

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))
(* 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
0.0ms	x	@	-inf	((- (* x x) (* (* y 4) z)) (* x x))
0.0ms	x	@	inf	((- (* x x) (* (* y 4) z)) (* x x))
0.0ms	x	@	0	((- (* x x) (* (* y 4) z)) (* x x))
0.0ms	y	@	inf	((- (* x x) (* (* y 4) z)) (* x x))
0.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* x x))

simplify169.0ms (2.6%)

Memory

-17.4MiB live, 291.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	79
1	89	79
2	273	79
3	1357	79
4	4981	79
0	8137	72

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 9

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))
(* 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))
(* 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)

rewrite162.0ms (2.5%)

Memory

-13.8MiB live, 125.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
0	11	16
1	37	16
2	267	16
3	3014	16
0	8697	15

Stop Event

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

Counts

2 → 15

Calls

Call 1

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

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.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))))

eval3.0ms (0%)

Memory: 4.5MiB live, 4.5MiB allocated
Compiler: Compiled 320 to 71 computations (77.8% saved)

prune3.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	19	4	23

Accuracy

100.0%

Counts

23 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
✓	51.9%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) z) y))
✓	53.2%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
	3.5%	#s(approx (- (* x x) (* (* y 4) z)) (neg.f64 (*.f64 x x)))

Compiler

Compiled 132 to 68 computations (48.5% saved)

regimes51.0ms (0.8%)

Memory

-2.3MiB live, 49.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

36.0ms	x
2.0ms	z
2.0ms	y
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Results

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

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes43.0ms (0.6%)

Memory

-24.0MiB live, 21.9MiB allocated

Counts

4 → 2

Calls

Call 1

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

Calls

7 calls:

31.0ms	x
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	z
2.0ms	y

Results

Accuracy	Segments	Branch
72.6%	5	`(*.f64 y #s(literal 4 binary64))`
72.6%	3	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
88.2%	2	`(*.f64 x x)`
80.1%	2	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
88.2%	2	`x`
72.6%	5	`y`
68.0%	3	`z`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes9.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Accuracy

Total -32.2b remaining (-107.6%)

Threshold costs -32.2b (-107.6%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
53.2%	1	`z`
53.2%	1	`(*.f64 y #s(literal 4 binary64))`
53.2%	1	`y`
53.2%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
53.2%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
53.2%	1	`(*.f64 x x)`
53.2%	1	`x`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

bsearch8.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	200231.96634910756	744805.5453805595

Samples

4.0ms

80×

valid

Compiler

Compiled 152 to 134 computations (11.8% saved)

Precisions

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

ival-mult: 1.0ms (53.9% of total)

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

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

exact: 0.0ms (0% of total)

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

simplify18.0ms (0.3%)

Memory

-23.7MiB live, 21.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	31	53
2	68	53
3	152	53
4	243	53
5	288	53

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal 560000 binary64)) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 (*.f64 #s(literal -4 binary64) z) y)) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))

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

Outputs

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

(if (<=.f64 x #s(literal 560000 binary64)) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 (*.f64 #s(literal -4 binary64) z) y)) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))

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

soundness694.0ms (10.5%)

Memory

8.0MiB live, 426.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	82
1	89	82
2	273	82
3	1357	82
4	4981	82
0	8137	75
0	18	53
0	27	53
1	95	52
2	637	52
3	7204	52
0	8017	52
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×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 119 to 82 computations (31.1% saved)

preprocess48.0ms (0.7%)

Memory

29.6MiB live, 82.9MiB allocated

Remove

(sort y z)

(abs x)

Compiler

Compiled 156 to 84 computations (46.2% saved)

end8.0ms (0.1%)

Memory: -35.3MiB live, 10.7MiB 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%)

sample1.0s (15.1%)

explain164.0ms (2.5%)

preprocess28.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize25.0ms (0.4%)

series8.0ms (0.1%)

simplify131.0ms (2%)

rewrite211.0ms (3.2%)

eval78.0ms (1.2%)

prune7.0ms (0.1%)

simplify10.0ms (0.1%)

localize45.0ms (0.7%)

series8.0ms (0.1%)

simplify3.0s (45.3%)

rewrite246.0ms (3.7%)

eval29.0ms (0.4%)

prune9.0ms (0.1%)

simplify13.0ms (0.2%)

localize38.0ms (0.6%)

series4.0ms (0.1%)

simplify127.0ms (1.9%)

rewrite138.0ms (2.1%)

eval3.0ms (0%)

prune29.0ms (0.4%)

simplify23.0ms (0.4%)

localize19.0ms (0.3%)

series3.0ms (0%)

simplify169.0ms (2.6%)

rewrite162.0ms (2.5%)

eval3.0ms (0%)

prune3.0ms (0%)

regimes51.0ms (0.8%)

regimes43.0ms (0.6%)

regimes9.0ms (0.1%)

bsearch8.0ms (0.1%)

simplify18.0ms (0.3%)

soundness694.0ms (10.5%)

preprocess48.0ms (0.7%)

end8.0ms (0.1%)

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