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)

sample679.0ms (18.3%)

Results

500.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 274.0ms

ival-mult: 184.0ms (67.2% of total)

ival-sub: 71.0ms (25.9% of total)

const: 15.0ms (5.5% of total)

backward-pass: 3.0ms (1.1% of total)

Bogosity

preprocess23.0ms (0.6%)

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)

explain86.0ms (2.3%)

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

39.0ms

512×

valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 8.0ms (59% of total)

ival-sub: 5.0ms (36.9% of total)

const: 1.0ms (7.4% 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)

localize32.0ms (0.9%)

Localize:

Found 3 expressions of interest:

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

Results

19.0ms

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 (69.9% of total)

ival-sub: 1.0ms (17.5% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

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
0.0ms	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)

rewrite320.0ms (8.7%)

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 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 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.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)))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))))
(.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)

eval32.0ms (0.9%)

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

prune29.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	265	4	269

Accuracy

100.0%

Counts

269 → 4

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))
▶	60.5%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
▶	51.3%	(.f64 #s(literal 2 binary64) (.f64 x x))
▶	49.6%	#s(literal -1 binary64)

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify157.0ms (4.2%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x x))

Rules

2518×	`fnmadd-define`
2198×	`fmsub-define`
2010×	`fnmsub-define`
1884×	`fmm-def`
1504×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	42	58
2	106	58
3	268	58
4	460	58
5	636	58
6	1075	58
7	1777	58
8	4395	58
9	6801	58
10	7622	58
11	7896	58
12	7920	58
13	7920	58
0	8487	58

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
-1
(* 2 (* x x))
2
(* x x)
x
(* (/ 1 (+ (* (* x x) 2) 1)) (+ -1 (* (* x x) (* (* x x) 4))))
(/ 1 (+ (* (* x x) 2) 1))
1
(+ (* (* x x) 2) 1)
(* (* x x) 2)
(* x x)
x
2
(+ -1 (* (* x x) (* (* x x) 4)))
-1
(* (* x x) (* (* x x) 4))
(* (* x x) 4)
4

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
(* (/ 1 (+ (* (* x x) 2) 1)) (+ -1 (* (* x x) (* (* x x) 4))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 x x))))
(/ 1 (+ (* (* x x) 2) 1))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -2 binary64)))))
1
#s(literal 1 binary64)
(+ (* (* x x) 2) 1)
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(* (* x x) 2)
(.f64 #s(literal 2 binary64) (.f64 x x))
(* x x)
(*.f64 x x)
x
2
#s(literal 2 binary64)
(+ -1 (* (* x x) (* (* x x) 4)))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))))
-1
#s(literal -1 binary64)
(* (* x x) (* (* x x) 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))
(* (* x x) 4)
(.f64 (.f64 x x) #s(literal 4 binary64))
4
#s(literal 4 binary64)

localize69.0ms (1.9%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 4 binary64))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))
✓	accuracy	66.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

50.0ms

256×

valid

Compiler

Compiled 88 to 15 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 10.0ms (53.5% of total)

ival-div: 6.0ms (32.1% of total)

ival-add: 3.0ms (16% of total)

const: 1.0ms (5.3% of total)

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

series4.0ms (0.1%)

Counts

8 → 96

Calls

Call 1

Inputs
#<alt (* 2 (* x x))>
#<alt (* x x)>
#<alt (* (/ 1 (+ (* (* x x) 2) 1)) (+ -1 (* (* x x) (* (* x x) 4))))>
#<alt (/ 1 (+ (* (* x x) 2) 1))>
#<alt (+ (* (* x x) 2) 1)>
#<alt (* (* x x) 2)>
#<alt (* (* x x) (* (* x x) 4))>
#<alt (* (* x x) 4)>

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)>
#<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 1>
#<alt (+ 1 (* -2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 4 (pow x 2)) 2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 4 (* -8 (pow x 2)))) 2)))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/2 (/ 1/8 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/2 (/ 1/8 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/2 (/ 1/8 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/2 (/ 1/8 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* 2 (pow x 2)))>
#<alt (+ 1 (* 2 (pow x 2)))>
#<alt (+ 1 (* 2 (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 (* (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 (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* (/ 1 (+ (* (* x x) 2) 1)) (+ -1 (* (* x x) (* (* x x) 4))))
0.0ms	x	@	0	(* (/ 1 (+ (* (* x x) 2) 1)) (+ -1 (* (* x x) (* (* x x) 4))))
0.0ms	x	@	inf	(* (* x x) (* (* x x) 4))
0.0ms	x	@	inf	(/ 1 (+ (* (* x x) 2) 1))
0.0ms	x	@	0	(* (* x x) (* (* x x) 4))

rewrite350.0ms (9.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4908×	`-lowering-.f32`
4908×	`-lowering-.f64`
2646×	`/-lowering-/.f32`
2646×	`/-lowering-/.f64`
1086×	`frac-times`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	75	35
2	620	35
0	8648	35

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 458

Calls

Call 1

Inputs
(* 2 (* x x))
(* x x)
(* (/ 1 (+ (* (* x x) 2) 1)) (+ -1 (* (* x x) (* (* x x) 4))))
(/ 1 (+ (* (* x x) 2) 1))
(+ (* (* x x) 2) 1)
(* (* x x) 2)
(* (* x x) (* (* x x) 4))
(* (* x x) 4)

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

simplify215.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

2518×	`fma-lowering-fma.f32`
2518×	`fma-lowering-fma.f64`
1558×	`sum5-define`
1542×	`fma-define`
1534×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	565
1	123	458
2	319	456
3	813	456
4	2221	456
5	5479	456
0	8029	456

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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)
-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))))
1
(+ 1 (* -2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 4 (pow x 2)) 2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 4 (* -8 (pow x 2)))) 2)))
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (pow x 2))
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (pow x 2))
1
(+ 1 (* 2 (pow x 2)))
(+ 1 (* 2 (pow x 2)))
(+ 1 (* 2 (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))
(* (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))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (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)
-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))
1
#s(literal 1 binary64)
(+ 1 (* -2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -2 binary64))))
(+ 1 (* (pow x 2) (- (* 4 (pow x 2)) 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -2 binary64) (.f64 (.f64 x x) #s(literal 4 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 4 (* -8 (pow x 2)))) 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x x) #s(literal -8 binary64)))))))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 1/2 (/ 1/8 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* 2 (pow x 2)))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* 2 (pow x 2)))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+ 1 (* 2 (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))
(* (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))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4 binary64))))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))
(* 4 (pow x 2))
(.f64 (.f64 x x) #s(literal 4 binary64))

eval108.0ms (2.9%)

Compiler: Compiled 24440 to 1482 computations (93.9% saved)

prune110.0ms (3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	613	1	614
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	614	4	618

Accuracy

100.0%

Counts

618 → 4

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))
▶	12.7%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))
✓	51.3%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	49.6%	#s(literal -1 binary64)

Compiler

Compiled 34 to 22 computations (35.3% saved)

simplify168.0ms (4.5%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
✓	cost-diff	384	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))

Rules

2554×	`-lowering-.f32`
2554×	`-lowering-.f64`
1944×	`/-lowering-/.f32`
1944×	`/-lowering-/.f64`
1454×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	44
1	31	36
2	107	35
3	314	34
4	830	33
5	1743	33
6	2892	33
7	5726	33
0	8428	33

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))
(/ 1/2 (* x x))
1/2
(* x x)
x
(+ -1 (* (* x x) (* (* x x) 4)))
-1
(* (* x x) (* (* x x) 4))
(* (* x x) 4)
4

Outputs
(* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))
(+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(/ 1/2 (* x x))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
x
(+ -1 (* (* x x) (* (* x x) 4)))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 #s(literal 4 binary64) (.f64 x (.f64 x x)))))
-1
#s(literal -1 binary64)
(* (* x x) (* (* x x) 4))
(.f64 x (.f64 #s(literal 4 binary64) (.f64 x (.f64 x x))))
(* (* x x) 4)
(.f64 (.f64 x x) #s(literal 4 binary64))
4
#s(literal 4 binary64)

localize47.0ms (1.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 4 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
✓	accuracy	66.4%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))

Results

35.0ms

256×

valid

Compiler

Compiled 56 to 11 computations (80.4% saved)

Precisions

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

ival-mult: 7.0ms (66.7% of total)

ival-div: 2.0ms (19% of total)

ival-add: 1.0ms (9.5% of total)

const: 1.0ms (9.5% of total)

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

series5.0ms (0.1%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))>
#<alt (/ 1/2 (* x x))>
#<alt (* x x)>
#<alt (+ -1 (* (* x x) (* (* x x) 4)))>
#<alt (* (* x x) (* (* x x) 4))>
#<alt (* (* x x) 4)>

Outputs
#<alt (/ -1/2 (pow x 2))>
#<alt (/ (- (* 2 (pow x 4)) 1/2) (pow x 2))>
#<alt (/ (- (* 2 (pow x 4)) 1/2) (pow x 2))>
#<alt (/ (- (* 2 (pow x 4)) 1/2) (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))>
#<alt (* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))>
#<alt (* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))>
#<alt (* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))>
#<alt (* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (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)>
#<alt -1>
#<alt (- (* 4 (pow x 4)) 1)>
#<alt (- (* 4 (pow x 4)) 1)>
#<alt (- (* 4 (pow x 4)) 1)>
#<alt (* 4 (pow x 4))>
#<alt (* (pow x 4) (- 4 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 4 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 4 (/ 1 (pow x 4))))>
#<alt (* 4 (pow x 4))>
#<alt (* (pow x 4) (- 4 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 4 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 4 (/ 1 (pow x 4))))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 4))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>
#<alt (* 4 (pow x 2))>

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))
1.0ms	x	@	0	(* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))
0.0ms	x	@	0	(/ 1/2 (* x x))
0.0ms	x	@	inf	(/ 1/2 (* x x))
0.0ms	x	@	-inf	(* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))

rewrite318.0ms (8.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3930×	`-lowering-.f32`
3930×	`-lowering-.f64`
2244×	`/-lowering-/.f32`
2244×	`/-lowering-/.f64`
1212×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	55	32
2	473	31
3	6204	31
0	8453	31

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 394

Calls

Call 1

Inputs
(* (/ 1/2 (* x x)) (+ -1 (* (* x x) (* (* x x) 4))))
(/ 1/2 (* x x))
(* x x)
(+ -1 (* (* x x) (* (* x x) 4)))
(* (* x x) (* (* x x) 4))
(* (* x x) 4)

Outputs
(+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
(-.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -2 binary64)) (.f64 x x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -4 binary64))))) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) (/.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 x (/.f64 #s(literal 1/2 binary64) x))))
(-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x x))) (/.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 x (.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 2 binary64) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(fma.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (/.f64 (.f64 x x) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (/.f64 #s(literal 2 binary64) (.f64 x x)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 2 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (/.f64 (.f64 x x) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) (.f64 x (.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) #s(literal 4 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(neg.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))))))
(neg.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -2 binary64))) (*.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))))))
(/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))))) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64))))))))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 (.f64 x x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))))))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))))) (/.f64 (.f64 x x) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))) (/.f64 x (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))))))
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(.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64)))))))
(.f64 (+.f64 #s(literal 1 binary64) (.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 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -4 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -16 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -4 binary64))))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (.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 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)))))))
(.f64 (+.f64 #s(literal -1 binary64) (.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 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 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 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -16 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -16 binary64)))) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64)))))))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.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 (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 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)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 16 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 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 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.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 (.f64 x x) (.f64 x (.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 (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -4 binary64))))
(neg.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -4 binary64))))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))
(.f64 x (.f64 (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 4 binary64))))
(.f64 (.f64 x x) (.f64 (.f64 x (*.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -4 binary64))))
(.f64 #s(literal 4 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64)))
(.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 x x))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (.f64 x x) #s(literal -4 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64))))))
(.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -4 binary64))) #s(literal -1 binary64))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 4 binary64))
(.f64 (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))) x)
(.f64 (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))) (*.f64 x #s(literal 1 binary64)))
(.f64 (.f64 x #s(literal 4 binary64)) (.f64 x (.f64 x x)))
(.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 4 binary64)))
(.f64 (.f64 x (.f64 x x)) (.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) x) (neg.f64 (.f64 x (.f64 x (.f64 x #s(literal 4 binary64))))))
(.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -4 binary64))
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (.f64 x (.f64 x (.f64 x #s(literal 4 binary64)))))
(.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -4 binary64))) (.f64 x x))
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal 4 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 4 binary64)))) (*.f64 x x))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 4 binary64))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 4 binary64))))) x)
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (*.f64 x #s(literal 4 binary64)))
(.f64 x (.f64 x #s(literal 4 binary64)))
(.f64 (.f64 x x) #s(literal 4 binary64))
(.f64 #s(literal 4 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 4 binary64)) x)

simplify180.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2832×	`fnmadd-define`
1738×	`sum3-define`
1316×	`fmsub-define`
1220×	`fma-lowering-fma.f32`
1220×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	392
1	53	344
2	115	344
3	241	344
4	495	344
5	1008	344
6	1990	344
7	3339	344
8	5506	344
0	8082	344

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(/ -1/2 (pow x 2))
(/ (- (* 2 (pow x 4)) 1/2) (pow x 2))
(/ (- (* 2 (pow x 4)) 1/2) (pow x 2))
(/ (- (* 2 (pow x 4)) 1/2) (pow x 2))
(* 2 (pow x 2))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(* 2 (pow x 2))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (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
(- (* 4 (pow x 4)) 1)
(- (* 4 (pow x 4)) 1)
(- (* 4 (pow x 4)) 1)
(* 4 (pow x 4))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(* 4 (pow x 4))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))
(* 4 (pow x 2))

Outputs
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ (- (* 2 (pow x 4)) 1/2) (pow x 2))
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (- (* 2 (pow x 4)) 1/2) (pow x 2))
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (- (* 2 (pow x 4)) 1/2) (pow x 2))
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* (pow x 2) (- 2 (* 1/2 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 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)
-1
#s(literal -1 binary64)
(- (* 4 (pow x 4)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(- (* 4 (pow x 4)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(- (* 4 (pow x 4)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* (pow x 4) (- 4 (/ 1 (pow x 4))))
(+.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 4))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))
(* 4 (pow x 2))
(.f64 x (.f64 x #s(literal 4 binary64)))

eval131.0ms (3.5%)

Compiler: Compiled 16844 to 1247 computations (92.6% saved)

prune69.0ms (1.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	526	0	526
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	526	4	530

Accuracy

100.0%

Counts

530 → 4

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))
✓	12.7%	(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 4 binary64)))))
✓	51.3%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	49.6%	#s(literal -1 binary64)

Compiler

Compiled 86 to 40 computations (53.5% saved)

regimes9.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

regimes4.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	(*.f64 x x)
1.0ms	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%)

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
49.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch14.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.03600533514045933	15878131744647834.0

Results

8.0ms

160×

valid

Compiler

Compiled 92 to 79 computations (14.1% saved)

Precisions

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

ival-mult: 2.0ms (55.8% of total)

ival-sub: 1.0ms (27.9% of total)

const: 0.0ms (0% of total)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	17	20
2	20	20
3	24	20

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

#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 1/2 binary64)) #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (*.f64 x x)))
(if (<=.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal -1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))
#s(literal -1 binary64)

soundness356.0ms (9.6%)

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×	done
1×	iter limit
1×	node limit

Compiler

Compiled 31 to 17 computations (45.2% saved)

preprocess26.0ms (0.7%)

Remove: (abs x)
Compiler: Compiled 90 to 54 computations (40% saved)

Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

analyze0.0ms (0%)

sample679.0ms (18.3%)

preprocess23.0ms (0.6%)

explain86.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize32.0ms (0.9%)

series2.0ms (0%)

rewrite320.0ms (8.7%)

simplify146.0ms (3.9%)

eval32.0ms (0.9%)

prune29.0ms (0.8%)

simplify157.0ms (4.2%)

localize69.0ms (1.9%)

series4.0ms (0.1%)

rewrite350.0ms (9.5%)

simplify215.0ms (5.8%)

eval108.0ms (2.9%)

prune110.0ms (3%)

simplify168.0ms (4.5%)

localize47.0ms (1.3%)

series5.0ms (0.1%)

rewrite318.0ms (8.6%)

simplify180.0ms (4.9%)

eval131.0ms (3.5%)

prune69.0ms (1.9%)

regimes9.0ms (0.2%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

bsearch14.0ms (0.4%)

simplify7.0ms (0.2%)

soundness356.0ms (9.6%)

preprocess26.0ms (0.7%)

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

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