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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.1s (28.4%)

Memory

22.0MiB live, 1 122.2MiB allocated; 193ms collecting garbage

Samples

697.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 333.0ms

ival-mult: 204.0ms (61.2% of total)

ival-sub: 113.0ms (33.9% of total)

ival-true: 5.0ms (1.5% of total)

exact: 5.0ms (1.5% of total)

ival-assert: 4.0ms (1.2% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

explain124.0ms (3.3%)

Memory

-3.7MiB live, 96.5MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`	nan-rescue	4	0
↳	`(*.f64 x x)`	overflow	77
↳	`(*.f64 y #s(literal 4 binary64))`	overflow	1
↳	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	overflow	33
`*.f64`	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	5	0
-	0	251

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	251
1	5

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms

512×

valid

Compiler

Compiled 61 to 28 computations (54.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 27.0ms (89.8% of total)

ival-sub: 2.0ms (6.7% of total)

ival-true: 1.0ms (3.3% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess48.0ms (1.3%)

Memory

-8.0MiB live, 34.1MiB allocated; 15ms collecting garbage

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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

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)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series9.0ms (0.2%)

Memory

12.4MiB live, 12.4MiB allocated; 0ms collecting garbage

Counts

8 → 14

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

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) x (* (* y 4) z) (* y 4) y 4 z)
1.0ms	y	@	0	((- (* x x) (* (* y 4) z)) (* x x) x (* (* y 4) z) (* y 4) y 4 z)
1.0ms	y	@	inf	((- (* x x) (* (* y 4) z)) (* x x) x (* (* y 4) z) (* y 4) y 4 z)
1.0ms	x	@	inf	((- (* x x) (* (* y 4) z)) (* x x) x (* (* y 4) z) (* y 4) y 4 z)
1.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* x x) x (* (* y 4) z) (* y 4) y 4 z)

simplify240.0ms (6.5%)

Memory

25.1MiB live, 215.4MiB allocated; 36ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	90
1	89	90
2	273	90
3	1359	90
4	4964	90
0	8120	83

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 11

Calls

Call 1

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

rewrite181.0ms (4.9%)

Memory

3.0MiB live, 238.6MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	12	24
1	38	24
2	268	24
3	3015	24
0	8706	23

Stop Event

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

Counts

8 → 387

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 (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)))
(/.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)))
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(.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))
y
#s(literal 4 binary64)
z

eval102.0ms (2.8%)

Memory: -21.4MiB live, 126.8MiB allocated; 32ms collecting garbage
Compiler: Compiled 11 965 to 900 computations (92.5% saved)

prune9.0ms (0.2%)

Memory

-19.2MiB live, 26.7MiB allocated; 4ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	404	3	407
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	405	3	408

Accuracy

100.0%

Counts

408 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
▶	98.8%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
▶	52.5%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 z y) #s(literal -4 binary64)))

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series8.0ms (0.2%)

Memory

18.6MiB live, 18.6MiB allocated; 0ms collecting garbage

Counts

13 → 19

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

simplify107.0ms (2.9%)

Memory

-1.8MiB live, 185.3MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	119
1	127	119
2	406	119
3	1591	119
4	5241	119
0	8107	108

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 16

Calls

Call 1

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

rewrite173.0ms (4.7%)

Memory

11.5MiB live, 350.5MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	57
0	27	57
1	95	56
2	637	56
3	7204	56
0	8017	56

Stop Event

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

Counts

13 → 453

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

eval59.0ms (1.6%)

Memory: -24.2MiB live, 134.8MiB allocated; 55ms collecting garbage
Compiler: Compiled 7 196 to 620 computations (91.4% saved)

prune15.0ms (0.4%)

Memory

-4.3MiB live, 43.9MiB allocated; 3ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	307	3	310

Accuracy

100.0%

Counts

310 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
✓	98.8%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
▶	52.5%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z))

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series5.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated; 0ms collecting garbage

Counts

6 → 12

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z))
(.f64 (.f64 #s(literal -4 binary64) y) z)
(*.f64 #s(literal -4 binary64) y)
#s(literal -4 binary64)
y
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))
(* -4 y)
y
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
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	@	inf	((- (* x x) (* (* y 4) z)) (* (* -4 y) z) (* -4 y) -4 y z)
1.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* (* -4 y) z) (* -4 y) -4 y z)
1.0ms	z	@	-inf	((- (* x x) (* (* y 4) z)) (* (* -4 y) z) (* -4 y) -4 y z)
1.0ms	z	@	inf	((- (* x x) (* (* y 4) z)) (* (* -4 y) z) (* -4 y) -4 y z)
1.0ms	y	@	0	((- (* x x) (* (* y 4) z)) (* (* -4 y) z) (* -4 y) -4 y z)

simplify130.0ms (3.5%)

Memory

8.3MiB live, 241.6MiB allocated; 24ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	84
1	89	84
2	273	84
3	1359	84
4	4976	84
0	8110	77

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 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))
(* -4 y)
y
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
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))
(* -4 y)
(*.f64 #s(literal -4 binary64) y)
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
(* 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)

rewrite152.0ms (4.1%)

Memory

1.8MiB live, 188.9MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
0	14	26
1	44	26
2	278	26
3	3048	26
0	8837	25

Stop Event

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

Counts

6 → 29

Calls

Call 1

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

eval3.0ms (0.1%)

Memory: 10.9MiB live, 10.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 557 to 93 computations (83.3% saved)

prune7.0ms (0.2%)

Memory

-28.9MiB live, 14.5MiB allocated; 8ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	34	4	38

Accuracy

100.0%

Counts

38 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
✓	98.8%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
✓	52.5%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z))
▶	52.6%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 44 to 36 computations (18.2% saved)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series3.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB allocated; 0ms collecting garbage

Counts

3 → 10

Calls

Call 1

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

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

simplify245.0ms (6.6%)

Memory

21.1MiB live, 351.2MiB allocated; 85ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	80
1	89	80
2	273	80
3	1357	80
4	4981	80
0	8137	73

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 9

Calls

Call 1

Inputs
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
x
(* (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)
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)

rewrite117.0ms (3.2%)

Memory

-6.9MiB live, 220.2MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
0	11	17
1	37	17
2	267	17
3	3014	17
0	8697	16

Stop Event

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

Counts

3 → 28

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 (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))))
(*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(neg.f64 x)
(sqrt.f64 (*.f64 x x))
(fabs.f64 x)
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 x))
(+.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (log.f64 x)))
x

eval5.0ms (0.1%)

Memory: 19.2MiB live, 19.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 742 to 136 computations (81.7% saved)

prune22.0ms (0.6%)

Memory

-35.5MiB live, 13.5MiB allocated; 21ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	45	5	50

Accuracy

100.0%

Counts

50 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
✓	98.8%	(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
✓	52.5%	#s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z))
	3.8%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 (neg.f64 x) x))
✓	52.6%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 140 to 74 computations (47.1% saved)

regimes46.0ms (1.3%)

Memory

25.7MiB live, 112.0MiB allocated; 23ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Calls

7 calls:

14.0ms	y
11.0ms	z
11.0ms	(.f64 (.f64 y #s(literal 4 binary64)) z)
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	x

Results

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

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes24.0ms (0.7%)

Memory

8.5MiB live, 52.0MiB allocated; 11ms collecting garbage

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

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

Calls

7 calls:

12.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
2.0ms	z
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	y
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
98.8%	1	`(*.f64 y #s(literal 4 binary64))`
98.8%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
98.8%	1	`(*.f64 x x)`
98.8%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`z`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes37.0ms (1%)

Memory

-10.6MiB live, 36.8MiB allocated; 31ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Calls

7 calls:

26.0ms	(.f64 (.f64 y #s(literal 4 binary64)) z)
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	z
2.0ms	y
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Results

Accuracy	Segments	Branch
67.3%	3	`(*.f64 y #s(literal 4 binary64))`
71.1%	3	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
84.8%	2	`(*.f64 x x)`
78.0%	2	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
84.8%	2	`x`
67.3%	3	`y`
69.5%	3	`z`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes10.0ms (0.3%)

Memory

29.9MiB live, 29.9MiB allocated; 0ms collecting garbage

Accuracy

Total -31.8b remaining (-104.9%)

Threshold costs -31.8b (-104.9%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

7 calls:

2.0ms	(*.f64 x x)
1.0ms	(*.f64 y #s(literal 4 binary64))
1.0ms	y
1.0ms	z
1.0ms	x

Results

Accuracy	Segments	Branch
52.6%	1	`(*.f64 y #s(literal 4 binary64))`
52.6%	1	`y`
52.6%	1	`z`
52.6%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
52.6%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
52.6%	1	`(*.f64 x x)`
52.6%	1	`x`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

bsearch12.0ms (0.3%)

Memory

-28.3MiB live, 22.4MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.00011297634542720198	0.0014422128962406472

Samples

7.0ms

96×

valid

Compiler

Compiled 180 to 158 computations (12.2% saved)

Precisions

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

ival-mult: 2.0ms (82.4% of total)

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

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

simplify16.0ms (0.4%)

Memory

-6.6MiB live, 36.8MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	61
1	31	61
2	68	61
3	152	61
4	243	61
5	288	61

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
(if (<=.f64 x #s(literal 5534023222112865/4611686018427387904 binary64)) #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z)) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Outputs
(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
(fma.f64 x x (.f64 (.f64 #s(literal -4 binary64) y) z))
(if (<=.f64 x #s(literal 5534023222112865/4611686018427387904 binary64)) #s(approx (- (* x x) (* (* y 4) z)) (.f64 (.f64 #s(literal -4 binary64) y) z)) #s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x)))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

derivations680.0ms (18.4%)

Memory

0.3MiB live, 531.1MiB allocated; 149ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	90
1	89	90
2	273	90
3	1359	90
4	4964	90
0	8120	83
0	18	57
0	27	57
1	95	56
2	637	56
3	7204	56
0	8017	56
0	8	24
0	12	24
1	38	24
2	268	24
3	3015	24
0	8706	23
0	36	84
1	89	84
2	273	84
3	1359	84
4	4976	84
0	8110	77

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 61 to 20 computations (67.2% saved)

preprocess56.0ms (1.5%)

Memory

5.3MiB live, 49.7MiB allocated; 11ms collecting garbage

Remove

(sort y z)

(abs x)

Compiler

Compiled 172 to 84 computations (51.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

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%)

sample1.1s (28.4%)

explain124.0ms (3.3%)

preprocess48.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series9.0ms (0.2%)

simplify240.0ms (6.5%)

rewrite181.0ms (4.9%)

eval102.0ms (2.8%)

prune9.0ms (0.2%)

simplify0.0ms (0%)

series8.0ms (0.2%)

simplify107.0ms (2.9%)

rewrite173.0ms (4.7%)

eval59.0ms (1.6%)

prune15.0ms (0.4%)

simplify0.0ms (0%)

series5.0ms (0.1%)

simplify130.0ms (3.5%)

rewrite152.0ms (4.1%)

eval3.0ms (0.1%)

prune7.0ms (0.2%)

simplify0.0ms (0%)

series3.0ms (0.1%)

simplify245.0ms (6.6%)

rewrite117.0ms (3.2%)

eval5.0ms (0.1%)

prune22.0ms (0.6%)

regimes46.0ms (1.3%)

regimes24.0ms (0.7%)

regimes37.0ms (1%)

regimes10.0ms (0.3%)

bsearch12.0ms (0.3%)

simplify16.0ms (0.4%)

derivations680.0ms (18.4%)

preprocess56.0ms (1.5%)

end0.0ms (0%)

Profiling

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