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

0.6MiB live, 0.6MiB 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)

sample777.0ms (17%)

Memory

41.1MiB live, 1 099.1MiB allocated

Samples

520.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-mult: 196.0ms (78% of total)

ival-sub: 40.0ms (15.9% of total)

ival-true: 6.0ms (2.4% of total)

exact: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain89.0ms (1.9%)

Memory

10.3MiB live, 132.5MiB 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))`
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	4	0
↳	`(*.f64 x x)`	overflow	67
↳	`(*.f64 y #s(literal 4 binary64))`	overflow	1
↳	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	overflow	28

Confusion

	Predicted +	Predicted -
+	4	0
-	0	252

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	4	0	0
-	0	0	252

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	252
1	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 85 to 36 computations (57.6% saved)

Precisions

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

ival-mult: 10.0ms (77.9% of total)

ival-sub: 2.0ms (15.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess59.0ms (1.3%)

Memory

-20.9MiB live, 55.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	99	84
2	273	81
3	630	81
4	965	81
5	1093	81
6	1137	81
7	1137	81
0	8	9
0	12	9
1	21	9
2	51	9
3	101	9
4	136	9
5	178	9
6	238	9
7	297	9
8	398	9
9	453	9
10	483	9
0	483	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

0.7MiB live, 0.7MiB 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)

simplify14.0ms (0.3%)

Memory

19.2MiB live, 19.2MiB 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	128	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	297	24
8	398	24
9	453	24
10	483	24
0	483	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 (0.5%)

Memory

-1.6MiB live, 34.7MiB 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	0.9023396216604116	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Samples

18.0ms

256×

valid

Compiler

Compiled 50 to 18 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 9.0ms (86.3% of total)

ival-sub: 1.0ms (9.6% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB 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	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))

simplify124.0ms (2.7%)

Memory

-39.6MiB live, 101.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	79
1	96	79
2	282	79
3	1068	79
4	3103	79
5	5929	79
6	7721	79
0	8070	72

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

rewrite189.0ms (4.1%)

Memory

3.0MiB live, 271.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	12	20
1	36	20
2	242	20
3	2285	20
0	8420	19

Stop Event

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

Counts

4 → 199

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.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 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.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 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) #s(literal -1 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 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 z y) (.f64 #s(literal 4 binary64) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z y) (.f64 #s(literal 4 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))) (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)))) (-.f64 (.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 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)))) (fma.f64 (.f64 z y) #s(literal -4 binary64) (*.f64 x x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #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 (.f64 #s(literal 4 binary64) y)) (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (*.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (*.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))))
(.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 -1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.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 -1 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 z y) #s(literal -4 binary64) (*.f64 x x)))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)))) (pow.f64 (neg.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (neg.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 (neg.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 -1 binary64)))
(.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (/.f64 (fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x)) (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)) (.f64 (fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x)) (pow.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (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 -1 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 (.f64 z y) #s(literal -4 binary64) (.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 (.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) #s(literal -4 binary64) (.f64 x x)) (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 -1 binary64))))
(.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 -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64))) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 z (.f64 #s(literal 4 binary64) y))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (.f64 x x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (.f64 x x)) (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (.f64 x x)) (.f64 #s(literal 0 binary64) (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x))))))
(/.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))) (pow.f64 (neg.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 3 binary64))) (+.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 (.f64 (neg.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)))) (neg.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))))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (neg.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))))))))
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(-.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)))) (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 (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 x #s(literal 8 binary64)) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 4 binary64)) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 binary64)) (.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 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))) (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 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 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))) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 18 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))) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 9 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))) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))) (neg.f64 (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.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 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.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 (/.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (/.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 4 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (/.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 binary64)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 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 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z (.f64 x x)) (.f64 #s(literal -4 binary64) y))))) (/.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 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 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z (.f64 x x)) (.f64 #s(literal -4 binary64) y))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z (.f64 x x)) (.f64 #s(literal -4 binary64) y))))) (/.f64 (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 9 binary64)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z (.f64 x x)) (.f64 #s(literal -4 binary64) y))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z (.f64 x x)) (.f64 #s(literal -4 binary64) y))))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z (.f64 x x)) (.f64 #s(literal -4 binary64) y))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 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 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 6 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 (/.f64 (pow.f64 x #s(literal 18 binary64)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 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 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 9 binary64)) (fma.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (fma.f64 #s(literal -64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 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 x x #s(literal 0 binary64)) (.f64 z (.f64 #s(literal 4 binary64) y)))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x)))
(-.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 (/.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 (.f64 x x) (.f64 z (*.f64 #s(literal 4 binary64) y)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (.f64 z y) #s(literal -4 binary64) (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 z (.f64 #s(literal 4 binary64) y) (.f64 x x))) (neg.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)))))
(+.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)))) (neg.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))))))
(+.f64 (.f64 (.f64 z y) #s(literal -4 binary64)) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 (*.f64 z y) #s(literal -4 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.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 x) #s(literal 2 binary64)))
(.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 (.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 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) y))))
(.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 (.f64 z #s(literal 4 binary64)))))
(.f64 (pow.f64 z #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal 4 binary64) y) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) y) #s(literal 1 binary64)) (pow.f64 z #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 z y) #s(literal 1 binary64)) #s(literal 4 binary64))
(.f64 (pow.f64 (.f64 z #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)))
(.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 (.f64 z #s(literal 4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 z y) #s(literal 4 binary64))
(.f64 (.f64 z #s(literal 4 binary64)) y)
(.f64 z (.f64 #s(literal 4 binary64) y))
(.f64 (.f64 #s(literal 4 binary64) y) z)
(.f64 #s(literal 4 binary64) (pow.f64 (.f64 z y) #s(literal 1 binary64)))
(.f64 #s(literal 4 binary64) (.f64 z y))
(.f64 y (.f64 z #s(literal 4 binary64)))
(pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 1 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 #s(literal 4 binary64) y)
(*.f64 y #s(literal 4 binary64))

eval65.0ms (1.4%)

Memory: 1.8MiB live, 44.0MiB allocated
Compiler: Compiled 8 139 to 626 computations (92.3% saved)

prune3.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	203	2	205

Accuracy

100.0%

Counts

205 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
▶	53.1%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify15.0ms (0.3%)

Memory

15.7MiB live, 15.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(*.f64 #s(literal -4 binary64) z)
cost-diff	0	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
cost-diff	0	(*.f64 z y)
cost-diff	0	(.f64 (.f64 z y) #s(literal -4 binary64))
cost-diff	0	#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	15	44
0	21	44
1	38	43
2	65	43
3	104	43
4	140	43
5	182	43
6	242	43
7	304	43
8	404	43
9	459	43
10	489	43
0	489	43

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

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

localize60.0ms (1.3%)

Memory

-32.7MiB live, 43.6MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 #s(literal -4 binary64) z)
accuracy	0.49999449521112044	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
accuracy	0.0	(*.f64 z y)
accuracy	0.010097509768442016	(.f64 (.f64 z y) #s(literal -4 binary64))
accuracy	30.02325232977062	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Samples

31.0ms

256×

valid

Compiler

Compiled 85 to 31 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 19.0ms (86% of total)

ival-sub: 1.0ms (4.5% of total)

ival-add: 1.0ms (4.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

6 → 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 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
(*.f64 #s(literal -4 binary64) z)
(*.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)
(* 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) (+ (* (* -4 z) y) (* x x)) (* -4 z) (* x x))
1.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) (* x x)) (* -4 z) (* x x))
1.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) (* x x)) (* -4 z) (* x x))
1.0ms	z	@	0	((- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) (* x x)) (* -4 z) (* x x))
1.0ms	x	@	0	((- (* x x) (* (* y 4) z)) (* (* z y) -4) (* z y) (+ (* (* -4 z) y) (* x x)) (* -4 z) (* x x))

simplify152.0ms (3.3%)

Memory

16.0MiB live, 97.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	113
1	134	113
2	393	113
3	1203	113
4	3343	113
5	6789	113
0	8159	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)
(* 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)
(* 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))

rewrite1.1s (23.5%)

Memory

-2.1MiB live, 113.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	37
0	21	37
1	63	36
2	421	36
3	4831	36
0	8952	36

Stop Event

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

Counts

6 → 266

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

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) z) y))
(.f64 (exp.f64 (log.f64 (neg.f64 y))) (exp.f64 (log.f64 (.f64 z #s(literal 4 binary64)))))
(.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (.f64 z (*.f64 #s(literal 4 binary64) y)))
(.f64 (exp.f64 (log.f64 (neg.f64 z))) (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) y))))
(.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 #s(literal -4 binary64) z))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) y))) (exp.f64 (log.f64 (neg.f64 z))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal -4 binary64) y))) (exp.f64 (log.f64 z)))
(.f64 (exp.f64 (log.f64 (.f64 z y))) (exp.f64 (log.f64 #s(literal -4 binary64))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal -4 binary64) z))) (exp.f64 (log.f64 y)))
(.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (.f64 #s(literal -4 binary64) y))))
(.f64 (.f64 (neg.f64 z) y) #s(literal 4 binary64))
(.f64 (.f64 (neg.f64 y) z) #s(literal 4 binary64))
(.f64 (.f64 #s(literal -1 binary64) (*.f64 z y)) #s(literal 4 binary64))
(.f64 (.f64 z (neg.f64 y)) #s(literal 4 binary64))
(.f64 (.f64 z #s(literal -1 binary64)) (*.f64 #s(literal 4 binary64) y))
(.f64 (neg.f64 (.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 #s(literal -1 binary64) (.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 (.f64 #s(literal -4 binary64) z) y)
(.f64 #s(literal -4 binary64) (.f64 z y))
(.f64 (.f64 z y) #s(literal -4 binary64))
(.f64 (.f64 z (*.f64 #s(literal 4 binary64) y)) #s(literal -1 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 y) z))
(.f64 #s(literal 4 binary64) (.f64 y (neg.f64 z)))
(.f64 #s(literal 4 binary64) (neg.f64 (.f64 z y)))
(.f64 y (.f64 #s(literal -4 binary64) z))
(pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 1 binary64))
(/.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y))))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (neg.f64 (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))))
(neg.f64 (.f64 z (.f64 #s(literal 4 binary64) y)))
(-.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal -4 binary64) z) y)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (.f64 (.f64 #s(literal -4 binary64) z) y)))
(+.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal -4 binary64) z) 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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.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 (.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.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 z y) #s(literal 4 binary64) (.f64 x x)))) (-.f64 (.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (*.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))) (-.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal 2 binary64))))) (-.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) (*.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))) (fma.f64 (pow.f64 (.f64 z y) #s(literal 6 binary64)) #s(literal 4096 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal 3 binary64))))) (fma.f64 (.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) (.f64 x x)) (-.f64 (.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) (.f64 x x)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64))) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)))) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #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 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x)))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #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 (.f64 #s(literal 4 binary64) y)) (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (*.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64))))
(.f64 (pow.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 #s(literal 64 binary64) (pow.f64 (.f64 z y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (-.f64 (pow.f64 (.f64 (*.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal -4 binary64) y) z (*.f64 x x)))
(.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 #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (neg.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 (neg.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) (/.f64 (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 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) (.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64))) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (*.f64 x x))))
(.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.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 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (pow.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (/.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 z y) #s(literal 4 binary64) (*.f64 x x))))
(.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) (.f64 (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 4 binary64))) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 6 binary64))) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))))) (neg.f64 (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))))) (neg.f64 (fma.f64 #s(literal 256 binary64) (pow.f64 (.f64 z y) #s(literal 4 binary64)) (fma.f64 #s(literal 16 binary64) (pow.f64 (.f64 z (.f64 (*.f64 x x) y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))))))
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(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))))
(fma.f64 #s(literal -1 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x))
(fma.f64 (.f64 z #s(literal 4 binary64)) (neg.f64 y) (.f64 x x))
(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))
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(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))))
(fma.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) (/.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.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 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 2 binary64)) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))))
(fma.f64 (.f64 #s(literal -4 binary64) z) (/.f64 (neg.f64 (.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) y)) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))))))
(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
(fma.f64 #s(literal -4 binary64) (/.f64 (neg.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal -4 binary64))) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))))))
(fma.f64 #s(literal -4 binary64) (.f64 z y) (.f64 x x))
(fma.f64 (.f64 z y) (/.f64 (neg.f64 (.f64 #s(literal 16 binary64) (.f64 z y))) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (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)) #s(literal -1 binary64) (*.f64 x x))
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(fma.f64 z (.f64 #s(literal -4 binary64) y) (.f64 x x))
(fma.f64 (.f64 #s(literal 4 binary64) y) (neg.f64 z) (.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 (neg.f64 y) z) (.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 y (neg.f64 z)) (.f64 x x))
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(fma.f64 y (.f64 #s(literal -4 binary64) z) (.f64 x x))
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(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) z) y))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 z (.f64 #s(literal 4 binary64) y)))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) (*.f64 x x)))
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(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal -16 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))))
(-.f64 (.f64 x x) (.f64 z (*.f64 #s(literal 4 binary64) y)))
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(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) #s(literal 3 binary64)) (fma.f64 (.f64 z #s(literal 4 binary64)) (.f64 y (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (/.f64 #s(literal -16 binary64) (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (fma.f64 (.f64 z y) #s(literal 4 binary64) (.f64 x x))))))
(+.f64 (.f64 (.f64 #s(literal -4 binary64) z) y) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 (*.f64 #s(literal -4 binary64) z) y))
(*.f64 (neg.f64 z) #s(literal 4 binary64))
(.f64 #s(literal -1 binary64) (.f64 z #s(literal 4 binary64)))
(*.f64 #s(literal -4 binary64) z)
(*.f64 z #s(literal -4 binary64))
(*.f64 #s(literal 4 binary64) (neg.f64 z))
(neg.f64 (*.f64 z #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 z #s(literal 4 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.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 x) #s(literal 2 binary64)))

eval147.0ms (3.2%)

Memory: -9.4MiB live, 88.2MiB allocated
Compiler: Compiled 9 253 to 778 computations (91.6% saved)

prune39.0ms (0.9%)

Memory

-17.2MiB live, 21.3MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	271	1	272
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	271	3	274

Accuracy

100.0%

Counts

274 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

99.2%

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

✓

53.1%

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

▶

53.1%

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

Compiler

Compiled 38 to 31 computations (18.4% saved)

simplify15.0ms (0.3%)

Memory

17.9MiB live, 17.9MiB 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	27	26
2	59	26
3	98	26
4	135	26
5	177	26
6	237	26
7	299	26
8	399	26
9	454	26
10	484	26
0	484	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

localize28.0ms (0.6%)

Memory

-4.0MiB live, 32.7MiB 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	30.02325232977062	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) z) y))

Samples

22.0ms

256×

valid

Compiler

Compiled 48 to 25 computations (47.9% saved)

Precisions

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

ival-mult: 9.0ms (85.2% of total)

ival-sub: 1.0ms (9.5% 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

6.7MiB live, 6.7MiB 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	@	inf	((- (* x x) (* (* y 4) z)) (* (* -4 z) y) (* -4 z))

simplify110.0ms (2.4%)

Memory

1.6MiB live, 116.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	74
1	96	74
2	282	74
3	1068	74
4	3118	74
5	5947	74
6	7739	74
0	8081	67

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

rewrite284.0ms (6.2%)

Memory

0.5MiB live, 244.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
0	14	23
1	42	23
2	250	23
3	2284	23
0	8335	22

Stop Event

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

Counts

3 → 42

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) z) y))
(.f64 (.f64 (neg.f64 z) y) #s(literal 4 binary64))
(.f64 (.f64 (neg.f64 y) z) #s(literal 4 binary64))
(.f64 (.f64 #s(literal -1 binary64) (*.f64 z y)) #s(literal 4 binary64))
(.f64 (.f64 z (neg.f64 y)) #s(literal 4 binary64))
(.f64 (.f64 z #s(literal -1 binary64)) (*.f64 #s(literal 4 binary64) y))
(.f64 (neg.f64 (.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 #s(literal -1 binary64) (.f64 z (*.f64 #s(literal 4 binary64) y)))
(.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 (.f64 z (*.f64 #s(literal 4 binary64) y)) #s(literal -1 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 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 (.f64 #s(literal -4 binary64) z))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 (*.f64 #s(literal -4 binary64) z) y)))))
(/.f64 (neg.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y))) (neg.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y))))) (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64))))
(/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (neg.f64 (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))))
(/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))))))
(/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y))))))
(neg.f64 (.f64 z (.f64 #s(literal 4 binary64) y)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))) (/.f64 (pow.f64 (.f64 z (.f64 #s(literal 4 binary64) y)) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal 16 binary64) (.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))))) (.f64 (.f64 #s(literal -4 binary64) z) y))
(-.f64 #s(literal 0 binary64) (.f64 z (.f64 #s(literal 4 binary64) y)))
(+.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal -4 binary64) z) y))
(*.f64 (neg.f64 z) #s(literal 4 binary64))
(.f64 #s(literal -1 binary64) (.f64 z #s(literal 4 binary64)))
(*.f64 #s(literal -4 binary64) z)
(*.f64 z #s(literal -4 binary64))
(*.f64 #s(literal 4 binary64) (neg.f64 z))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 z #s(literal 4 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 #s(literal 16 binary64) (.f64 z z) (.f64 #s(literal 0 binary64) (.f64 z #s(literal 4 binary64))))))
(neg.f64 (*.f64 z #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 z #s(literal 4 binary64)))

eval8.0ms (0.2%)

Memory: -25.2MiB live, 11.7MiB allocated
Compiler: Compiled 899 to 152 computations (83.1% saved)

prune3.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	46	3	49

Accuracy

100.0%

Counts

49 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
✓	53.1%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))
▶	51.1%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 36 to 29 computations (19.4% saved)

simplify15.0ms (0.3%)

Memory

26.4MiB live, 26.4MiB 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	20	17
2	50	17
3	100	17
4	137	17
5	179	17
6	239	17
7	299	17
8	399	17
9	454	17
10	484	17
0	484	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

localize20.0ms (0.4%)

Memory

-4.8MiB live, 32.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	31.32441628766619	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Samples

14.0ms

256×

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

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

ival-mult: 5.0ms (82.1% of total)

ival-sub: 1.0ms (16.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB 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))

simplify115.0ms (2.5%)

Memory

-13.1MiB live, 111.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	71
1	96	71
2	282	71
3	1068	71
4	3118	71
5	5947	71
6	7739	71
0	8081	64

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

rewrite189.0ms (4.1%)

Memory

2.6MiB live, 231.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
0	11	16
1	35	16
2	241	16
3	2274	16
0	8407	15

Stop Event

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

Counts

2 → 7

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 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.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 x) #s(literal 2 binary64)))

eval1.0ms (0%)

Memory: 1.6MiB live, 1.6MiB allocated
Compiler: Compiled 151 to 35 computations (76.8% saved)

prune2.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	10	3	13

Accuracy

100.0%

Counts

13 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (.f64 #s(literal -4 binary64) z) y (.f64 x x))
✓	53.1%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))
✓	51.1%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 96 to 51 computations (46.9% saved)

regimes30.0ms (0.7%)

Memory

-26.6MiB live, 22.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

7 calls:

17.0ms	x
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	z
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
2.0ms	y

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)

regimes12.0ms (0.3%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

Results

Accuracy	Segments	Branch
84.1%	2	`x`
70.8%	5	`y`
66.4%	3	`z`
77.6%	2	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
84.1%	2	`(*.f64 x x)`
71.0%	3	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
70.8%	5	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes8.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
51.1%	1	`z`
51.1%	1	`y`
51.1%	1	`(*.f64 y #s(literal 4 binary64))`
51.1%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
51.1%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
51.1%	1	`x`
51.1%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

bsearch18.0ms (0.4%)

Memory

-25.7MiB live, 12.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.6050308937036337e-66	1.6996019604512666e-57

Samples

11.0ms

144×

valid

Compiler

Compiled 246 to 221 computations (10.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 7.0ms (86.6% of total)

ival-sub: 1.0ms (12.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify121.0ms (2.6%)

Memory

12.7MiB live, 48.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	55
1	27	55
2	56	55
3	107	55
4	153	55
5	208	55
6	353	55
7	4705	55

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x x) #s(literal 7350083789478079/56539106072908298546665520023773392506479484700019806659891398441363832832 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 (*.f64 #s(literal -4 binary64) z) y (*.f64 x x))

(if (<=.f64 (*.f64 x x) #s(literal 7350083789478079/56539106072908298546665520023773392506479484700019806659891398441363832832 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))

soundness719.0ms (15.7%)

Memory

9.0MiB live, 402.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	12	20
1	36	20
2	242	20
3	2285	20
0	8420	19
0	15	37
0	21	37
1	63	36
2	421	36
3	4831	36
0	8952	36
0	36	74
1	96	74
2	282	74
3	1068	74
4	3118	74
5	5947	74
6	7739	74
0	8081	67
0	36	79
1	96	79
2	282	79
3	1068	79
4	3103	79
5	5929	79
6	7721	79
0	8070	72

Stop Event

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

Compiler

Compiled 138 to 91 computations (34.1% saved)

preprocess27.0ms (0.6%)

Memory

11.3MiB live, 48.2MiB allocated

Remove

(sort y z)

(abs x)

Compiler

Compiled 160 to 80 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	297	24
8	398	24
9	453	24
10	483	24
0	483	23

Iter	Nodes	Cost
0	15	44
0	21	44
1	38	43
2	65	43
3	104	43
4	140	43
5	182	43
6	242	43
7	304	43
8	404	43
9	459	43
10	489	43
0	489	43

Iter	Nodes	Cost
0	12	26
0	14	26
1	27	26
2	59	26
3	98	26
4	135	26
5	177	26
6	237	26
7	299	26
8	399	26
9	454	26
10	484	26
0	484	25

Iter	Nodes	Cost
0	10	17
0	11	17
1	20	17
2	50	17
3	100	17
4	137	17
5	179	17
6	239	17
7	299	17
8	399	17
9	454	17
10	484	17
0	484	16

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	297	24
8	398	24
9	453	24
10	483	24
0	483	23

Iter	Nodes	Cost
0	15	44
0	21	44
1	38	43
2	65	43
3	104	43
4	140	43
5	182	43
6	242	43
7	304	43
8	404	43
9	459	43
10	489	43
0	489	43

Iter	Nodes	Cost
0	12	26
0	14	26
1	27	26
2	59	26
3	98	26
4	135	26
5	177	26
6	237	26
7	299	26
8	399	26
9	454	26
10	484	26
0	484	25

Iter	Nodes	Cost
0	10	17
0	11	17
1	20	17
2	50	17
3	100	17
4	137	17
5	179	17
6	239	17
7	299	17
8	399	17
9	454	17
10	484	17
0	484	16

start0.0ms (0%)

analyze0.0ms (0%)

sample777.0ms (17%)

explain89.0ms (1.9%)

preprocess59.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify14.0ms (0.3%)

localize23.0ms (0.5%)

series7.0ms (0.2%)

simplify124.0ms (2.7%)

rewrite189.0ms (4.1%)

eval65.0ms (1.4%)

prune3.0ms (0.1%)

simplify15.0ms (0.3%)

localize60.0ms (1.3%)

series6.0ms (0.1%)

simplify152.0ms (3.3%)

rewrite1.1s (23.5%)

eval147.0ms (3.2%)

prune39.0ms (0.9%)

simplify15.0ms (0.3%)

localize28.0ms (0.6%)

series4.0ms (0.1%)

simplify110.0ms (2.4%)

rewrite284.0ms (6.2%)

eval8.0ms (0.2%)

prune3.0ms (0.1%)

simplify15.0ms (0.3%)

localize20.0ms (0.4%)

series3.0ms (0.1%)

simplify115.0ms (2.5%)

rewrite189.0ms (4.1%)

eval1.0ms (0%)

prune2.0ms (0.1%)

regimes30.0ms (0.7%)

regimes12.0ms (0.3%)

regimes8.0ms (0.2%)

bsearch18.0ms (0.4%)

simplify121.0ms (2.6%)

soundness719.0ms (15.7%)

preprocess27.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	24
0	12	24
1	21	24
2	51	24
3	101	24
4	136	24
5	178	24
6	238	24
7	297	24
8	398	24
9	453	24
10	483	24
0	483	23

Iter	Nodes	Cost
0	15	44
0	21	44
1	38	43
2	65	43
3	104	43
4	140	43
5	182	43
6	242	43
7	304	43
8	404	43
9	459	43
10	489	43
0	489	43

Iter	Nodes	Cost
0	12	26
0	14	26
1	27	26
2	59	26
3	98	26
4	135	26
5	177	26
6	237	26
7	299	26
8	399	26
9	454	26
10	484	26
0	484	25

Iter	Nodes	Cost
0	10	17
0	11	17
1	20	17
2	50	17
3	100	17
4	137	17
5	179	17
6	239	17
7	299	17
8	399	17
9	454	17
10	484	17
0	484	16