Metrics for Expression 3, p15

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 17 to 9 computations (47.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

ival-<=: 0.0ms (0% of total)

sample789.0ms (31.2%)

Results

531.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 295.0ms

ival-mult: 149.0ms (50.6% of total)

ival-<=: 75.0ms (25.5% of total)

ival-add: 41.0ms (13.9% of total)

ival-and: 17.0ms (5.8% of total)

const: 11.0ms (3.7% of total)

backward-pass: 2.0ms (0.7% of total)

Bogosity

preprocess71.0ms (2.8%)

Algorithm

2×	egg-herbie

Rules

668×	`fnmadd-define`
538×	`fnmsub-define`
534×	`fmsub-define`
382×	`fmm-def`
364×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	48	18
2	162	18
3	599	18
4	1496	18
5	2233	18
6	2344	18
0	4	6
1	15	6
2	26	6
3	35	6
4	49	6
5	77	6
6	83	6
0	83	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (* x (* x x)) (* x x))

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

Call 2

Inputs
(+ (* x (* x x)) (* x x))
(+ (* (neg x) (* (neg x) (neg x))) (* (neg x) (neg x)))
(neg (+ (* (neg x) (* (neg x) (neg x))) (* (neg x) (neg x))))

Outputs
(+ (* x (* x x)) (* x x))
(fma x (square x) (square x))
(+ (* (neg x) (* (neg x) (neg x))) (* (neg x) (neg x)))
(fmsub x x (pow x 3))
(neg (+ (* (neg x) (* (neg x) (neg x))) (* (neg x) (neg x))))
(fmsub x (square x) (square x))

explain61.0ms (2.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`(.f64 x (.f64 x x))`
-	-	`(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))`

Results

36.0ms

512×

valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

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

ival-mult: 7.0ms (67% of total)

ival-add: 2.0ms (19.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 8 to 5 computations (37.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 18 to 9 computations (50% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

42×	`-lowering-.f32`
42×	`-lowering-.f64`
40×	`fma-define`
28×	`fma-lowering-fma.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	27	27
2	39	27
3	62	27
4	66	27
0	66	27

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x (* x (+ x 1)))
x
(* x (+ x 1))
(+ x 1)
1
(+ (* x (* x x)) (* x x))
(* x (* x x))
x
(* x x)

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

localize46.0ms (1.8%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))

Results

36.0ms

256×

valid

Compiler

Compiled 37 to 9 computations (75.7% saved)

Precisions

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

ival-mult: 6.0ms (62.7% of total)

ival-add: 3.0ms (31.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series4.0ms (0.1%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (* x (* x (+ x 1)))>
#<alt (* x (+ x 1))>
#<alt (+ x 1)>
#<alt (+ (* x (* x x)) (* x x))>
#<alt (* x (* x x))>
#<alt (* x x)>

Outputs
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

18 calls:

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

rewrite48.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

56×	`fma-define`
50×	`-lowering-.f32`
50×	`-lowering-.f64`
40×	`fma-lowering-fma.f32`
40×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	29	24
2	47	24
3	78	24
4	110	24
5	141	24
6	179	24
7	193	24
0	193	24

Stop Event

1×	iter limit
1×	saturated

Counts

6 → 60

Calls

Call 1

Inputs
(* x (* x (+ x 1)))
(* x (+ x 1))
(+ x 1)
(+ (* x (* x x)) (* x x))
(* x (* x x))
(* x x)

Outputs
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64) (*.f64 x x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) x)
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))
(+.f64 x (*.f64 x x))
(+.f64 (*.f64 x x) x)
(fma.f64 x x x)
(fma.f64 x #s(literal 1 binary64) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) x (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) x)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) x)
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64))))
(*.f64 (+.f64 x #s(literal 1 binary64)) x)
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64) (*.f64 x x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) x)
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))

simplify292.0ms (11.6%)

Algorithm

1×	egg-herbie

Rules

4678×	`-lowering-.f32`
4678×	`-lowering-.f64`
4214×	`cube-prod`
3010×	`/-lowering-/.f32`
3010×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	298
1	49	255
2	86	255
3	244	255
4	1407	255
5	2398	255
6	3219	255
7	3634	255
8	4031	255
9	4507	255
10	4999	255
11	5541	255
12	5731	255
13	5776	255
14	5776	255
15	6177	255
16	6782	255
17	7466	255
0	8009	255

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(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
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
x
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.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)
(pow x 2)
(*.f64 x x)

eval15.0ms (0.6%)

Compiler: Compiled 1208 to 97 computations (92% saved)

prune6.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	148	4	152

Accuracy

100.0%

Counts

152 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (.f64 x (.f64 x x)))
▶	100.0%	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
▶	100.0%	(.f64 x (+.f64 (.f64 x x) x))
▶	98.4%	(*.f64 x x)

Compiler

Compiled 29 to 15 computations (48.3% saved)

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	6400	(fma.f64 x x (.f64 x (.f64 x x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) x)
✓	cost-diff	0	(.f64 x (+.f64 (.f64 x x) x))
✓	cost-diff	0	(*.f64 x x)

Rules

64×	`fma-define`
42×	`-lowering-.f32`
42×	`-lowering-.f64`
28×	`fma-lowering-fma.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	41
1	25	41
2	36	41
3	50	41
4	78	41
5	85	41
0	85	41

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x x)
x
(* x (+ (* x x) x))
x
(+ (* x x) x)
(* x x)
(* (+ x 1) (* x x))
(+ x 1)
x
1
(* x x)
(+ (* x x) (* x (* x x)))
x
(* x (* x x))
(* x x)

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

localize68.0ms (2.7%)

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x (.f64 x (.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	accuracy	100.0%	(+.f64 (*.f64 x x) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 x (+.f64 (.f64 x x) x))
✓	accuracy	100.0%	(*.f64 x x)

Results

41.0ms

256×

valid

Compiler

Compiled 54 to 10 computations (81.5% saved)

Precisions

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

ival-mult: 8.0ms (49.4% of total)

ival-add: 4.0ms (24.7% of total)

compiled-spec: 3.0ms (18.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0.1%)

Counts

7 → 84

Calls

Call 1

Inputs
#<alt (* x x)>
#<alt (* x (+ (* x x) x))>
#<alt (+ (* x x) x)>
#<alt (* (+ x 1) (* x x))>
#<alt (+ x 1)>
#<alt (+ (* x x) (* x (* x x)))>
#<alt (* x (* x x))>

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

21 calls:

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

rewrite25.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

84×	`fma-define`
50×	`-lowering-.f32`
50×	`-lowering-.f64`
40×	`fma-lowering-fma.f32`
40×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	27	30
2	44	30
3	64	30
4	109	30
5	135	30
6	179	30
7	216	30
0	216	30

Stop Event

1×	iter limit
1×	saturated

Counts

7 → 75

Calls

Call 1

Inputs
(* x x)
(* x (+ (* x x) x))
(+ (* x x) x)
(* (+ x 1) (* x x))
(+ x 1)
(+ (* x x) (* x (* x x)))
(* x (* x x))

Outputs
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 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))
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64) (*.f64 x x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) x)
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
(.f64 (.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 x (*.f64 x x))
(+.f64 (*.f64 x x) x)
(fma.f64 x x x)
(fma.f64 x #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) x)
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64))))
(*.f64 (+.f64 x #s(literal 1 binary64)) x)
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64) (*.f64 x x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) x)
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
(.f64 (.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64) (*.f64 x x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) x)
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
(.f64 (.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))

simplify557.0ms (22.1%)

Algorithm

1×	egg-herbie

Rules

4678×	`-lowering-.f32`
4678×	`-lowering-.f64`
4214×	`cube-prod`
3010×	`/-lowering-/.f32`
3010×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	370
1	49	317
2	86	317
3	244	317
4	1407	317
5	2398	317
6	3219	317
7	3634	317
8	4031	317
9	4507	317
10	4999	317
11	5541	317
12	5731	317
13	5776	317
14	5776	317
15	6177	317
16	6782	317
17	7466	317
0	8009	317

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

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)
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

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)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
x
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval20.0ms (0.8%)

Compiler: Compiled 1535 to 100 computations (93.5% saved)

prune7.0ms (0.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	213	4	217

Accuracy

100.0%

Counts

217 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (.f64 x (.f64 x x)))
✓	100.0%	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	100.0%	(.f64 x (+.f64 (.f64 x x) x))
✓	98.4%	(*.f64 x x)

Compiler

Compiled 71 to 27 computations (62% saved)

regimes33.0ms (1.3%)

Counts

6 → 1

Calls

Call 1

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

Outputs
(fma.f64 x x (.f64 x (.f64 x x)))

Calls

2 calls:

30.0ms	x
2.0ms	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))`

Compiler

Compiled 12 to 5 computations (58.3% saved)

regimes4.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))

Calls

2 calls:

2.0ms	x
2.0ms	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))`

Compiler

Compiled 12 to 5 computations (58.3% saved)

regimes2.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(.f64 x (+.f64 (.f64 x x) x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	21	34

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness414.0ms (16.4%)

Rules

4678×	`-lowering-.f32`
4678×	`-lowering-.f64`
4214×	`cube-prod`
3010×	`/-lowering-/.f32`
3010×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	15	6
2	26	6
3	35	6
4	49	6
5	77	6
6	83	6
0	83	6
0	8	25
1	29	24
2	47	24
3	78	24
4	110	24
5	141	24
6	179	24
7	193	24
0	193	24
0	14	298
1	49	255
2	86	255
3	244	255
4	1407	255
5	2398	255
6	3219	255
7	3634	255
8	4031	255
9	4507	255
10	4999	255
11	5541	255
12	5731	255
13	5776	255
14	5776	255
15	6177	255
16	6782	255
17	7466	255
0	8009	255

Stop Event

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

Compiler

Compiled 88 to 41 computations (53.4% saved)

preprocess34.0ms (1.3%)

Compiler: Compiled 106 to 40 computations (62.3% saved)

Expression 3, p15

analyze0.0ms (0%)

sample789.0ms (31.2%)

preprocess71.0ms (2.8%)

explain61.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.3%)

localize46.0ms (1.8%)

series4.0ms (0.1%)

rewrite48.0ms (1.9%)

simplify292.0ms (11.6%)

eval15.0ms (0.6%)

prune6.0ms (0.2%)

simplify12.0ms (0.5%)

localize68.0ms (2.7%)

series2.0ms (0.1%)

rewrite25.0ms (1%)

simplify557.0ms (22.1%)

eval20.0ms (0.8%)

prune7.0ms (0.3%)

regimes33.0ms (1.3%)

regimes4.0ms (0.2%)

regimes2.0ms (0.1%)

regimes2.0ms (0.1%)

regimes1.0ms (0.1%)

simplify7.0ms (0.3%)

soundness414.0ms (16.4%)

preprocess34.0ms (1.3%)

end0.0ms (0%)

Profiling