Metrics for Data.Random.Dice:roll from dice-0.1

analyze0.0ms (0%)

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 5 computations (28.6% saved)

Precisions

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

ival-sub: 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)

sample485.0ms (18.4%)

Results

329.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 142.0ms

ival-mult: 87.0ms (61.2% of total)

ival-sub: 42.0ms (29.6% of total)

const: 10.0ms (7% of total)

backward-pass: 3.0ms (2.1% of total)

Bogosity

preprocess224.0ms (8.5%)

Algorithm

2×	egg-herbie

Rules

1992×	`fmsub-define`
1904×	`sum4-define`
1738×	`sum3-define`
1722×	`fmm-def`
1712×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	31	13
2	87	12
3	227	12
4	663	12
5	2609	12
6	5275	12
7	7500	12
0	4	4
1	14	4
2	18	4
3	33	4
4	74	4
5	258	4
6	507	4
7	1111	4
8	3682	4
9	7799	4
0	8080	4

Stop Event

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

Calls

Call 1

Inputs
(- (* x x) 1)

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

Call 2

Inputs
(- (* x x) 1)
(- (* (neg x) (neg x)) 1)
(neg (- (* (neg x) (neg x)) 1))

Outputs
(- (* x x) 1)
(fmsub x x 1)
(- (* (neg x) (neg x)) 1)
(fmsub x x 1)
(neg (- (* (neg x) (neg x)) 1))
(fnmsub x x -1)

Symmetry

(abs x)

explain52.0ms (2%)

FPErrors

Click to see full error table

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

Results

23.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

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

ival-mult: 5.0ms (53.3% of total)

ival-sub: 4.0ms (42.6% of total)

const: 1.0ms (10.7% of total)

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

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

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)

simplify154.0ms (5.8%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

1992×	`fmsub-define`
1722×	`fmm-def`
1712×	`fma-lowering-fma.f32`
1712×	`fma-lowering-fma.f64`
1664×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
1	14	9
2	18	9
3	33	9
4	74	9
5	258	9
6	507	9
7	1111	9
8	3682	9
9	7799	9
0	8080	9

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- (* x x) 1)
(* x x)
x
1

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

localize17.0ms (0.6%)

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)

Results

11.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (48.7% of total)

ival-sub: 1.0ms (24.4% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

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

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

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)

rewrite452.0ms (17.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3176×	`/-lowering-/.f32`
3176×	`/-lowering-/.f64`
2130×	`fma-lowering-fma.f32`
2130×	`fma-lowering-fma.f64`
2042×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	29	7
2	169	7
3	1663	7
0	8230	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 285

Calls

Call 1

Inputs
(- (* x x) 1)
(* x x)

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

simplify147.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1672×	`fnmadd-define`
1562×	`-lowering-.f32`
1562×	`-lowering-.f64`
1460×	`fmsub-define`
1422×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	18	79
2	42	79
3	96	79
4	322	79
5	570	79
6	1143	79
7	4645	79
0	8230	79

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

eval39.0ms (1.5%)

Compiler: Compiled 16304 to 779 computations (95.2% saved)

prune48.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	307	2	309
Fresh	0	0	0
Picked	0	1	1
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
✓	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
▶	49.1%	(*.f64 x x)
▶	51.9%	#s(literal -1 binary64)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)

Rules

2×	`-lowering-.f32`
2×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	3	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-1
(* x x)
x

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

localize15.0ms (0.6%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)

Results

11.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

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

ival-mult: 2.0ms (76.4% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* 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)>

Calls

3 calls:

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

rewrite152.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1432×	`prod-exp`
1304×	`-lowering-.f32`
1304×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	2	3
1	4	3
2	11	3
3	27	3
4	75	3
5	234	1
6	1655	1
7	1684	1
8	1814	1
9	3107	1
0	8343	1

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(* x x)

Outputs
#s(literal 1 binary64)
x

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`
2×	`-lowering-.f32`
2×	`-lowering-.f64`
2×	`unpow2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

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)

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)

eval1.0ms (0.1%)

Compiler: Compiled 39 to 3 computations (92.3% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	13	4	17

Accuracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
✓	49.1%	(*.f64 x x)
▶	4.6%	x
✓	51.9%	#s(literal -1 binary64)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
x

Outputs
x

localize11.0ms (0.4%)

Results

4.0ms

256×

valid

Compiler

Compiled 3 to 2 computations (33.3% saved)

Precisions

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

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite9.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Accuracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
✓	49.1%	(*.f64 x x)
✓	4.6%	x
✓	51.9%	#s(literal -1 binary64)

Compiler

Compiled 25 to 14 computations (44% saved)

regimes6.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(-.f64 (*.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)

regimes29.0ms (1.1%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

27.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.2%	2	`x`
99.2%	2	`(*.f64 x x)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes2.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
x

Outputs
#s(literal -1 binary64)
x

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
54.9%	2	`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
#s(literal -1 binary64)

Outputs
#s(literal -1 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
51.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.650592825097169e-15	6.201162375672361

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch10.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	5.1483908409299783e-8	2.4902133193106892

Results

5.0ms

144×

valid

Compiler

Compiled 64 to 52 computations (18.8% saved)

Precisions

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

ival-sub: 1.0ms (46.6% of total)

ival-mult: 1.0ms (46.6% of total)

const: 0.0ms (0% of total)

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

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`mul-1-neg_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	15	22
2	18	22
3	23	22

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) #s(literal -1 binary64) (.f64 x x))
(if (<=.f64 x #s(literal 1 binary64)) #s(literal -1 binary64) x)
#s(literal -1 binary64)

Outputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) #s(literal -1 binary64) (.f64 x x))
(if (<=.f64 x #s(literal 1 binary64)) #s(literal -1 binary64) x)
#s(literal -1 binary64)

soundness716.0ms (27.1%)

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1672×	`fnmadd-define`
1562×	`-lowering-.f32`
1562×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	18	79
2	42	79
3	96	79
4	322	79
5	570	79
6	1143	79
7	4645	79
0	8230	79
0	2	3
1	4	3
2	11	3
3	27	3
4	75	3
5	234	1
6	1655	1
7	1684	1
8	1814	1
9	3107	1
0	8343	1

Stop Event

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

Compiler

Compiled 39 to 21 computations (46.2% saved)

preprocess33.0ms (1.3%)

Remove: (abs x)
Compiler: Compiled 82 to 44 computations (46.3% saved)

Data.Random.Dice:roll from dice-0.1

analyze0.0ms (0%)

sample485.0ms (18.4%)

preprocess224.0ms (8.5%)

explain52.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify154.0ms (5.8%)

localize17.0ms (0.6%)

series1.0ms (0%)

rewrite452.0ms (17.1%)

simplify147.0ms (5.6%)

eval39.0ms (1.5%)

prune48.0ms (1.8%)

simplify4.0ms (0.2%)

localize15.0ms (0.6%)

series0.0ms (0%)

rewrite152.0ms (5.8%)

simplify5.0ms (0.2%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

simplify3.0ms (0.1%)

localize11.0ms (0.4%)

series0.0ms (0%)

rewrite9.0ms (0.3%)

simplify3.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes6.0ms (0.2%)

regimes29.0ms (1.1%)

regimes2.0ms (0.1%)

regimes1.0ms (0.1%)

bsearch0.0ms (0%)

bsearch10.0ms (0.4%)

simplify14.0ms (0.5%)

soundness716.0ms (27.1%)

preprocess33.0ms (1.3%)

end0.0ms (0%)

Profiling