Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

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 9 to 7 computations (22.2% 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)

sample781.0ms (20.8%)

Results

574.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 297.0ms

ival-mult: 211.0ms (71.1% of total)

ival-sub: 66.0ms (22.2% of total)

const: 17.0ms (5.7% of total)

backward-pass: 3.0ms (1% of total)

Bogosity

preprocess27.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

200×	`fmsub-define`
198×	`fnmsub-define`
198×	`fnmadd-define`
120×	`fmm-def`
94×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	36	16
2	88	15
3	201	15
4	442	15
5	622	15
6	740	15
7	764	15
0	6	5
1	17	5
2	25	5
3	27	5
0	27	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (* (* x x) 2) 1)

Outputs
(- (* (* x x) 2) 1)
(+.f64 (.f64 x (.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))

Call 2

Inputs
(- (* (* x x) 2) 1)
(- (* (* (neg x) (neg x)) 2) 1)
(neg (- (* (* (neg x) (neg x)) 2) 1))

Outputs
(- (* (* x x) 2) 1)
(fnmsub (square x) -2 1)
(- (* (* (neg x) (neg x)) 2) 1)
(fnmsub (square x) -2 1)
(neg (- (* (* (neg x) (neg x)) 2) 1))
(fnmsub 2 (square x) -1)

Symmetry

(abs x)

explain71.0ms (1.9%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(.f64 (.f64 x x) #s(literal 2 binary64))`
-	-	`(*.f64 x x)`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 2 binary64)`
-	-	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`

Results

43.0ms

512×

valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 8.0ms (64.1% of total)

ival-sub: 3.0ms (24% of total)

const: 1.0ms (8% of total)

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

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal 2 binary64))
✓	cost-diff	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
8×	`fma-lowering-fma.f32`
8×	`fmsub-define`
8×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	17	14
2	25	14
3	27	14
0	27	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (* (* x x) 2) 1)
(* (* x x) 2)
(* x x)
x
2
1

Outputs
(- (* (* x x) 2) 1)
(+.f64 (.f64 x (.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))
(* (* x x) 2)
(.f64 x (.f64 x #s(literal 2 binary64)))
(* x x)
(*.f64 x x)
x
2
#s(literal 2 binary64)
1
#s(literal 1 binary64)

localize30.0ms (0.8%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 2 binary64))

Results

22.0ms

256×

valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

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

ival-mult: 4.0ms (64.2% of total)

ival-sub: 1.0ms (16.1% of total)

const: 1.0ms (16.1% of total)

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

series4.0ms (0.1%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (- (* (* x x) 2) 1)>
#<alt (* (* x x) 2)>
#<alt (* x x)>

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

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(- (* (* x x) 2) 1)
0.0ms	x	@	0	(- (* (* x x) 2) 1)
0.0ms	x	@	0	(* (* x x) 2)
0.0ms	x	@	inf	(* (* x x) 2)
0.0ms	x	@	inf	(* x x)

rewrite371.0ms (9.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3202×	`-lowering-.f32`
3202×	`-lowering-.f64`
2924×	`/-lowering-/.f32`
2924×	`/-lowering-/.f64`
1520×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	31	11
2	185	11
3	1918	11
0	8400	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 232

Calls

Call 1

Inputs
(- (* (* x x) 2) 1)
(* (* x x) 2)
(* x x)

Outputs
(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 512 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 512 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal -2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 512 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal -2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal -2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64)))))) (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64)))))))
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(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64))) #s(literal 1 binary64)))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -2 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 512 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 64 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 64 binary64)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64))))))
(exp.f64 (log.f64 (.f64 (.f64 x x) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(.f64 x (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 x (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 (.f64 x #s(literal 2 binary64)) (*.f64 x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 x #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))) x)
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (.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 x (.f64 x #s(literal 1 binary64)))
(.f64 x (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))

simplify146.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2278×	`-lowering-.f32`
2278×	`-lowering-.f64`
1476×	`fnmadd-define`
1276×	`div-sub`
1074×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	161
1	22	126
2	46	126
3	111	126
4	247	126
5	413	126
6	979	126
7	3149	126
8	5538	126
0	8214	126

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

eval40.0ms (1.1%)

Compiler: Compiled 12906 to 685 computations (94.7% saved)

prune30.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	266	3	269

Accuracy

100.0%

Counts

269 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
▶	51.2%	(.f64 #s(literal 2 binary64) (.f64 x x))
▶	49.9%	#s(literal -1 binary64)

Compiler

Compiled 16 to 12 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x x))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
6×	`*-commutative`
2×	`associate-r`
2×	`square-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	9	9
2	12	9
0	12	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-1
(* 2 (* x x))
2
(* x x)
x

Outputs
-1
#s(literal -1 binary64)
(* 2 (* x x))
(.f64 #s(literal 2 binary64) (.f64 x x))
2
#s(literal 2 binary64)
(* x x)
(*.f64 x x)
x

localize29.0ms (0.8%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

23.0ms

256×

valid

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 4.0ms (84.6% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (* 2 (* x x))>
#<alt (* x x)>

Outputs
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (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	(* 2 (* x x))
0.0ms	x	@	0	(* 2 (* x x))
0.0ms	x	@	-inf	(* 2 (* x x))
0.0ms	x	@	0	(* x x)
0.0ms	x	@	-inf	(* x x)

rewrite162.0ms (4.3%)

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	4	6
1	9	6
2	19	6
3	36	6
4	94	6
5	288	2
6	1857	2
7	1889	2
8	2023	2
9	3324	2
0	8715	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 3

Calls

Call 1

Inputs
(* 2 (* x x))
(* x x)

Outputs
#s(literal 2 binary64)
#s(literal 1 binary64)
x

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
6×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	6	72
2	11	72
3	12	72
0	12	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 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)

Outputs
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.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)

eval2.0ms (0.1%)

Compiler: Compiled 128 to 7 computations (94.5% saved)

prune2.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	25	5	30

Accuracy

100.0%

Counts

30 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	51.2%	(.f64 #s(literal 2 binary64) (.f64 x x))
▶	4.5%	(*.f64 #s(literal 2 binary64) x)
▶	2.9%	#s(literal 2 binary64)
✓	49.9%	#s(literal -1 binary64)

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	4	6
0	4	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
2
(* 2 x)
2
x

Outputs
2
#s(literal 2 binary64)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x

localize32.0ms (0.9%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)

Results

21.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

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

ival-mult: 9.0ms (94.4% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* 2 x)>

Outputs
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* 2 x)
0.0ms	x	@	0	(* 2 x)
0.0ms	x	@	inf	(* 2 x)

rewrite9.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 2 x)

Outputs
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

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
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)

eval5.0ms (0.1%)

Compiler: Compiled 43 to 4 computations (90.7% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	14	5	19

Accuracy

100.0%

Counts

19 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	51.2%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	4.5%	(*.f64 #s(literal 2 binary64) x)
✓	2.9%	#s(literal 2 binary64)
✓	49.9%	#s(literal -1 binary64)

Compiler

Compiled 40 to 26 computations (35% saved)

regimes9.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Calls

4 calls:

2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
100.0%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes6.0ms (0.2%)

Counts

4 → 2

Calls

Call 1

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

Outputs
#s(literal -1 binary64)
(.f64 #s(literal 2 binary64) (.f64 x x))

Calls

2 calls:

4.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(*.f64 x x)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes2.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

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

Outputs
#s(literal -1 binary64)
(*.f64 #s(literal 2 binary64) x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
52.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
#s(literal 2 binary64)

Outputs
#s(literal -1 binary64)
#s(literal 2 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
51.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

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
49.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.772746007252776e-13	889413.8295689352

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch14.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	4.2103990395837493e-7	943.0873923284815

Results

9.0ms

144×

valid

Compiler

Compiled 84 to 72 computations (14.3% saved)

Precisions

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

ival-mult: 2.0ms (57.4% of total)

ival-sub: 1.0ms (28.7% of total)

const: 0.0ms (0% of total)

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

bsearch15.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	4.2103990395837493e-7	943.0873923284815

Results

9.0ms

144×

valid

Compiler

Compiled 66 to 63 computations (4.5% saved)

Precisions

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

ival-mult: 2.0ms (58.2% of total)

ival-sub: 1.0ms (29.1% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	23	34
2	26	34
3	31	34

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) x))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(literal -1 binary64) #s(literal 2 binary64))
#s(literal -1 binary64)

Outputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (*.f64 x x)))
(if (<=.f64 (.f64 x x) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal -1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) x))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(literal -1 binary64) #s(literal 2 binary64))
#s(literal -1 binary64)

soundness1.9s (50.4%)

Rules

2278×	`-lowering-.f32`
2278×	`-lowering-.f64`
2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1476×	`fnmadd-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	9	6
2	19	6
3	36	6
4	94	6
5	288	2
6	1857	2
7	1889	2
8	2023	2
9	3324	2
0	8715	2
0	10	161
1	22	126
2	46	126
3	111	126
4	247	126
5	413	126
6	979	126
7	3149	126
8	5538	126
0	8214	126

Stop Event

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

Compiler

Compiled 65 to 37 computations (43.1% saved)

preprocess34.0ms (0.9%)

Remove: (abs x)
Compiler: Compiled 118 to 64 computations (45.8% saved)

Iter	Nodes	Cost
0	11	16
1	36	16
2	88	15
3	201	15
4	442	15
5	622	15
6	740	15
7	764	15
0	6	5
1	17	5
2	25	5
3	27	5
0	27	5

Iter	Nodes	Cost
0	11	16
1	36	16
2	88	15
3	201	15
4	442	15
5	622	15
6	740	15
7	764	15
0	6	5
1	17	5
2	25	5
3	27	5
0	27	5

analyze0.0ms (0%)

sample781.0ms (20.8%)

preprocess27.0ms (0.7%)

explain71.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize30.0ms (0.8%)

series4.0ms (0.1%)

rewrite371.0ms (9.9%)

simplify146.0ms (3.9%)

eval40.0ms (1.1%)

prune30.0ms (0.8%)

simplify4.0ms (0.1%)

localize29.0ms (0.8%)

series0.0ms (0%)

rewrite162.0ms (4.3%)

simplify5.0ms (0.1%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

simplify3.0ms (0.1%)

localize32.0ms (0.9%)

series1.0ms (0%)

rewrite9.0ms (0.2%)

simplify4.0ms (0.1%)

eval5.0ms (0.1%)

prune3.0ms (0.1%)

regimes9.0ms (0.2%)

regimes6.0ms (0.2%)

regimes2.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch0.0ms (0%)

bsearch14.0ms (0.4%)

bsearch15.0ms (0.4%)

simplify9.0ms (0.2%)

soundness1.9s (50.4%)

preprocess34.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	11	16
1	36	16
2	88	15
3	201	15
4	442	15
5	622	15
6	740	15
7	764	15
0	6	5
1	17	5
2	25	5
3	27	5
0	27	5