Metrics for Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample566.0ms (13.9%)

Memory

64.8MiB live, 918.9MiB allocated

Samples

357.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 220.0ms

ival-mult: 167.0ms (75.8% of total)

ival-add: 40.0ms (18.2% of total)

ival-true: 6.0ms (2.7% of total)

exact: 5.0ms (2.3% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

preprocess17.0ms (0.4%)

Memory

1.1MiB live, 40.0MiB allocated

Algorithm

1×	egg-herbie

Rules

20×	`sub-neg`
16×	`distribute-lft-neg-in`
16×	`neg-mul-1`
14×	`associate--r+`
14×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	22	10
2	54	10
3	98	10
4	132	10
5	146	10
6	148	10
0	4	5
0	6	5
1	9	5
0	9	4

Stop Event

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

Calls

Call 1

Inputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))

Outputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))

Symmetry

(abs x)

explain56.0ms (1.4%)

Memory

-56.8MiB live, 129.9MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 1 binary64)`
-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

22.0ms

512×

valid

Compiler

Compiled 36 to 20 computations (44.4% saved)

Precisions

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

ival-mult: 4.0ms (57.9% of total)

ival-add: 2.0ms (29% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	128	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Rules

4×	`lower-+.f32`
2×	`lift-+.f64`
2×	`lower-fma.f64`
2×	`lower-+.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	9	10
0	9	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal 1 binary64)

Outputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal 1 binary64)

localize14.0ms (0.3%)

Memory

-4.7MiB live, 34.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)

Samples

9.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-mult: 2.0ms (59.9% of total)

ival-add: 1.0ms (29.9% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (+.f64 (*.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* x x) 1)
0.0ms	x	@	0	(+ (* x x) 1)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	0	(* x x)
0.0ms	x	@	-inf	(+ (* x x) 1)

rewrite493.0ms (12.1%)

Memory

0.3MiB live, 711.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

11 846×	`lower-fma.f64`
11 846×	`lower-fma.f32`
3 746×	`lower-/.f64`
3 746×	`lower-/.f32`
3 638×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	24	8
2	145	8
3	1172	8
0	8585	7

Stop Event

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

Counts

2 → 261

Calls

Call 1

Inputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)

Outputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x x))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (neg.f64 (.f64 x x))))
(+.f64 #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 (.f64 x x))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) x))
(+.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x (.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 x (fma.f64 x (.f64 x x) x))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x (neg.f64 x) #s(literal -1 binary64))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) x) (.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) x))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 x (fma.f64 x (.f64 x x) x))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 x (fma.f64 x (.f64 x x) x))) (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (*.f64 x x)))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x x) x))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x x) x))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))) (fma.f64 x x #s(literal 1 binary64))))
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(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (fma.f64 x (neg.f64 x) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 x (*.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (/.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))))))
(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (neg.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))

simplify967.0ms (23.7%)

Memory

16.9MiB live, 650.5MiB allocated

Algorithm

1×	egg-herbie

Rules

18 422×	`lower-fma.f64`
18 422×	`lower-fma.f32`
9 228×	`lower-*.f64`
9 228×	`lower-*.f32`
2 982×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	88
1	20	88
2	35	88
3	56	88
4	88	88
5	102	88
6	131	88
7	224	88
8	585	88
9	1594	88
10	3141	88
11	4984	88
12	5390	88
13	5742	88
14	6103	88
15	6286	88
0	8901	79

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

eval96.0ms (2.4%)

Memory: 1.3MiB live, 75.5MiB allocated
Compiler: Compiled 11 788 to 597 computations (94.9% saved)

prune81.0ms (2%)

Memory

14.8MiB live, 91.6MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	282	3	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	283	3	286

Accuracy

100.0%

Counts

286 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x #s(literal 1 binary64))
▶	47.2%	(*.f64 x x)
▶	56.2%	#s(literal 1 binary64)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x x)

Rules

4×	`lower-+.f64`
4×	`lower-+.f32`
2×	`1-exp`
2×	`lift-*.f64`
2×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	11
0	6	11
1	9	11
0	9	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 1 binary64)
(*.f64 x x)
x
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)
(*.f64 x x)
x
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)

localize39.0ms (1%)

Memory

-6.3MiB live, 30.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)

Samples

33.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 26.0ms (94.4% of total)

ival-add: 1.0ms (3.6% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x x)
0.0ms	x	@	-inf	(+ (* x x) 1)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	-inf	(* x x)
0.0ms	x	@	inf	(+ (* x x) 1)

rewrite397.0ms (9.7%)

Memory

-21.5MiB live, 750.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

11 846×	`lower-fma.f32`
11 844×	`lower-fma.f64`
3 746×	`lower-/.f64`
3 746×	`lower-/.f32`
3 638×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	24	7
2	145	7
3	1174	7
0	8602	7

Stop Event

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

Counts

2 → 261

Calls

Call 1

Inputs
(*.f64 x x)
(fma.f64 x x #s(literal 1 binary64))

Outputs
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
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(*.f64 #s(literal -1 binary64) (fma.f64 x (neg.f64 x) #s(literal -1 binary64)))
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(.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
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(.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))
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(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/2 binary64)))

simplify566.0ms (13.9%)

Memory

-3.0MiB live, 807.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 422×	`lower-fma.f64`
18 422×	`lower-fma.f32`
9 228×	`lower-*.f64`
9 228×	`lower-*.f32`
2 978×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	88
1	20	88
2	35	88
3	56	88
4	88	88
5	102	88
6	131	88
7	227	88
8	621	88
9	1646	88
10	3181	88
11	5028	88
12	5432	88
13	5784	88
14	6145	88
15	6328	88
0	8941	79

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))

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

eval58.0ms (1.4%)

Memory: -12.3MiB live, 62.6MiB allocated
Compiler: Compiled 11 748 to 588 computations (95% saved)

prune52.0ms (1.3%)

Memory

-1.2MiB live, 79.6MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	285	3	288

Accuracy

100.0%

Counts

288 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	47.2%	(*.f64 x x)
✓	56.2%	#s(literal 1 binary64)

Compiler

Compiled 25 to 12 computations (52% saved)

regimes6.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(*.f64 x x)
(fma.f64 x x #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal 1 binary64))

Outputs
(fma.f64 x x #s(literal 1 binary64))

Calls

3 calls:

2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes4.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(*.f64 x x)

Outputs
#s(literal 1 binary64)
(*.f64 x x)

Calls

3 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
99.4%	2	`(*.f64 x x)`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

3 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
56.2%	1	`x`
56.2%	1	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
56.2%	1	`(*.f64 x x)`

Compiler

Compiled 12 to 7 computations (41.7% saved)

bsearch12.0ms (0.3%)

Memory

-15.8MiB live, 23.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.003290220450749315	6.575266133585415e+23

Samples

5.0ms

176×

valid

Compiler

Compiled 75 to 63 computations (16% saved)

Precisions

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

ival-add: 2.0ms (107.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify6.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	9	15

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x x #s(literal 1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64) (.f64 x x))
#s(literal 1 binary64)

Outputs
(fma.f64 x x #s(literal 1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64) (.f64 x x))
#s(literal 1 binary64)

soundness597.0ms (14.6%)

Memory

-21.3MiB live, 250.8MiB allocated

Rules

18 422×	`lower-fma.f64`
18 422×	`lower-fma.f32`
11 846×	`lower-fma.f64`
11 846×	`lower-fma.f32`
9 228×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	88
1	20	88
2	35	88
3	56	88
4	88	88
5	102	88
6	131	88
7	224	88
8	585	88
9	1594	88
10	3141	88
11	4984	88
12	5390	88
13	5742	88
14	6103	88
15	6286	88
0	8901	79
0	4	8
0	6	8
1	24	8
2	145	8
3	1172	8
0	8585	7

Stop Event

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

Compiler

Compiled 29 to 15 computations (48.3% saved)

preprocess37.0ms (0.9%)

Memory: 16.1MiB live, 53.6MiB allocated
Remove: (abs x)
Compiler: Compiled 54 to 26 computations (51.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample566.0ms (13.9%)

preprocess17.0ms (0.4%)

explain56.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize14.0ms (0.3%)

series1.0ms (0%)

rewrite493.0ms (12.1%)

simplify967.0ms (23.7%)

eval96.0ms (2.4%)

prune81.0ms (2%)

simplify5.0ms (0.1%)

localize39.0ms (1%)

series1.0ms (0%)

rewrite397.0ms (9.7%)

simplify566.0ms (13.9%)

eval58.0ms (1.4%)

prune52.0ms (1.3%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch12.0ms (0.3%)

simplify6.0ms (0.1%)

soundness597.0ms (14.6%)

preprocess37.0ms (0.9%)

end0.0ms (0%)

Profiling