Metrics for Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2

analyze2.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

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

ival-mult: 2.0ms (106% of total)

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

const: 0.0ms (0% of total)

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

sample519.0ms (15.4%)

Results

347.0ms

8256×

valid

Precisions

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

ival-mult: 72.0ms (50.7% of total)

ival-sub: 57.0ms (40.2% of total)

const: 10.0ms (7% of total)

backward-pass: 2.0ms (1.4% of total)

Bogosity

preprocess44.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

360×	`sum5-define`
350×	`sum3-define`
346×	`fnmadd-define`
284×	`fnmadd-define`
272×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	26	16
2	65	15
3	220	12
4	621	12
5	1273	12
6	1366	12
7	1374	12
0	4	5
1	10	5
2	16	5
3	21	5
4	25	4
5	31	4
6	43	4
7	78	4
8	176	4
9	452	4
10	997	4
11	1087	4
12	1095	4
0	1095	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* x (- x 1))

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

Call 2

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

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

explain44.0ms (1.3%)

FPErrors

Click to see full error table

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

Results

29.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

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

ival-mult: 5.0ms (51.3% of total)

ival-sub: 3.0ms (30.8% of total)

const: 1.0ms (10.3% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

360×	`sum5-define`
350×	`sum3-define`
284×	`fnmadd-define`
184×	`fma-define`
166×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	10	10
2	16	10
3	21	10
4	25	9
5	31	9
6	43	9
7	78	9
8	176	9
9	452	9
10	997	9
11	1087	9
12	1095	9
0	1095	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize18.0ms (0.5%)

Localize:

Found 2 expressions of interest:

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

Results

12.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

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

ival-sub: 2.0ms (48.5% of total)

ival-mult: 2.0ms (48.5% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite304.0ms (9%)

Algorithm

1×	batch-egg-rewrite

Rules

3864×	`/-lowering-/.f32`
3864×	`/-lowering-/.f64`
2498×	`-lowering-.f32`
2498×	`-lowering-.f64`
1528×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	23	8
2	140	7
3	1310	7
0	8675	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 285

Calls

Call 1

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

Outputs
(+.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) x))
(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x x))
(+.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(-.f64 (*.f64 x x) x)
(-.f64 (/.f64 (*.f64 x x) #s(literal 1 binary64)) x)
(-.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) x)) (/.f64 (.f64 x x) (+.f64 (.f64 x x) x)))
(fma.f64 x x (-.f64 #s(literal 0 binary64) x))
(fma.f64 x (+.f64 x #s(literal -1 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 x #s(literal -1 binary64) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (+.f64 x #s(literal -1 binary64)) x (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x)))) x) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 x (+.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) x (*.f64 x x))
(fma.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (/.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x)))) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(fma.f64 (/.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))) (+.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) x) (-.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) x) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (-.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x x)))
(/.f64 (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))) (-.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x x)))
(/.f64 (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) x) (-.f64 (-.f64 #s(literal -1 binary64) x) (.f64 x x)))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) x) (-.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x x)) (+.f64 (*.f64 x x) x))
(/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))))) (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x x))) (neg.f64 (+.f64 (*.f64 x x) x)))
(/.f64 (neg.f64 (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (neg.f64 (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) x)) (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (neg.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) x)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (.f64 x (+.f64 x #s(literal -1 binary64))))) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) x) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) x) (+.f64 (-.f64 #s(literal 0 binary64) x) x)) (.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) x) x)))))
(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) x) (+.f64 (-.f64 #s(literal 0 binary64) x) x))) (-.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) x) x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))
(*.f64 (+.f64 x #s(literal -1 binary64)) x)
(.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 x (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x))
(.f64 (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 (.f64 x x) #s(literal -1 binary64)))
(.f64 (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (.f64 x (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
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(.f64 (/.f64 (+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))) (+.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))

simplify201.0ms (6%)

Algorithm

1×	egg-herbie

Rules

1786×	`fnmsub-define`
1774×	`-lowering-.f32`
1774×	`-lowering-.f64`
1722×	`fmsub-define`
1598×	`fmm-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	83
1	33	83
2	76	83
3	151	74
4	451	74
5	1998	74
6	4524	74
7	7333	74
0	8125	74

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

Outputs
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- x 1))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* x (- x 1))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* x (- x 1))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
-1
#s(literal -1 binary64)
(- x 1)
(+.f64 #s(literal -1 binary64) x)
(- x 1)
(+.f64 #s(literal -1 binary64) x)
(- x 1)
(+.f64 #s(literal -1 binary64) x)
x
(* x (- 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) x)
(* x (- 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) x)
(* x (- 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) x)
x
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 #s(literal -1 binary64) x)
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 #s(literal -1 binary64) x)
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 #s(literal -1 binary64) x)

eval84.0ms (2.5%)

Compiler: Compiled 8934 to 858 computations (90.4% saved)

prune68.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	306	3	309
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	306	4	310

Accuracy

100.0%

Counts

310 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (*.f64 x x) x)
▶	46.4%	(-.f64 #s(literal 0 binary64) x)
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
▶	55.7%	(*.f64 x x)

Compiler

Compiled 20 to 12 computations (40% saved)

simplify36.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

222×	`sum3-define`
168×	`fnmadd-define`
166×	`fmsub-define`
160×	`sum5-define`
156×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
1	10	16
2	18	16
3	41	16
4	79	16
5	125	16
6	373	16
7	549	16
8	700	16
9	788	16
10	796	16
0	796	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x x)
x
(- 0 x)
0
x
(- (* x x) x)
(* x x)
x

Outputs
(* x x)
(*.f64 x x)
x
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
x
(- (* x x) x)
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* x x)
(*.f64 x x)
x

localize29.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 (*.f64 x x) x)
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) x)
✓	accuracy	100.0%	(*.f64 x x)

Results

21.0ms

256×

valid

Compiler

Compiled 20 to 6 computations (70% saved)

Precisions

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

ival-sub: 2.0ms (37.7% of total)

ival-mult: 2.0ms (37.7% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (* x x)>
#<alt (- 0 x)>
#<alt (- (* x x) x)>

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

Calls

9 calls:

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

rewrite225.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1622×	`fma-lowering-fma.f32`
1622×	`fma-lowering-fma.f64`
1552×	`fmsub-define`
1532×	`fmm-def`
1336×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	34	9
2	284	9
3	4001	9
0	8058	9

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 312

Calls

Call 1

Inputs
(* x x)
(- 0 x)
(- (* x x) x)

Outputs
(+.f64 (*.f64 x x) #s(literal 0 binary64))
(+.f64 (*.f64 x x) (fma.f64 x #s(literal 0 binary64) #s(literal 0 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(-.f64 (*.f64 x x) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) x #s(literal 0 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x (.f64 x x)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) x))
(/.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x))) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) x)
(/.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
(/.f64 (.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))
(/.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (*.f64 x (+.f64 x #s(literal 1 binary64))))))))))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal 1 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x) (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x)) (+.f64 (.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal 1 binary64)))) (/.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal 1 binary64))))) (.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x) (/.f64 (.f64 x x) (*.f64 x (+.f64 x #s(literal 1 binary64))))))))
(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))) (.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))))) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (*.f64 x (+.f64 x #s(literal 1 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x) (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x)) (.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal 1 binary64)))) (/.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) x) (/.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x)) #s(literal 1 binary64)) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))) (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (*.f64 x x))))
(/.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64))))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x x)) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x x)))
(/.f64 (/.f64 (.f64 x (-.f64 (.f64 x (*.f64 x x)) x)) (+.f64 x #s(literal 1 binary64))) x)
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(*.f64 x (+.f64 #s(literal -1 binary64) x))
(.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x)) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))) (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) (*.f64 x (+.f64 x #s(literal 1 binary64))))))))
(.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64)))))) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))) (.f64 x (-.f64 (.f64 x (*.f64 x x)) x)))
(.f64 (/.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) x))
(.f64 (/.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) x)) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (.f64 x (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (.f64 x (.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))))))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (-.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x)) (.f64 (.f64 x (+.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))) (.f64 x (-.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 x #s(literal 1 binary64))))))) (.f64 x (-.f64 (.f64 x (.f64 x x)) (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(.f64 (/.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) x)) (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (-.f64 (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x x)) (.f64 x (.f64 x x))))

simplify221.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1882×	`-lowering-.f32`
1882×	`-lowering-.f64`
1288×	`fnmadd-define`
1222×	`fmsub-define`
1100×	`fmm-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	113
1	23	113
2	41	113
3	89	104
4	233	104
5	515	104
6	1193	104
7	3627	104
8	7284	104
0	8026	104

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

Outputs
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* x (- x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* x (- x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))

eval70.0ms (2.1%)

Compiler: Compiled 8961 to 689 computations (92.3% saved)

prune48.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	446	1	447
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	447	4	451

Accuracy

100.0%

Counts

451 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) x)
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
✓	55.7%	(*.f64 x x)
▶	46.4%	(neg.f64 x)

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(neg.f64 x)

Rules

8×	`sum3-define`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
6×	`--lowering--.f32`
6×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3
1	6	3
2	8	3
3	10	3
4	16	3
5	20	3
6	26	3
7	29	3
0	29	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(neg x)
x

Outputs
(neg x)
(-.f64 #s(literal 0 binary64) x)
x

localize12.0ms (0.4%)

Localize:

Found 1 expressions of interest:

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

Results

8.0ms

256×

valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

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

ival-neg: 1.0ms (59.6% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (neg x)>

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

Calls

3 calls:

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

rewrite123.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

510×	`/-lowering-/.f32`
510×	`/-lowering-/.f64`
434×	`-lowering-.f32`
434×	`-lowering-.f64`
238×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	6	2
2	21	2
3	150	2
0	1663	2

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

1 → 56

Calls

Call 1

Inputs
(neg x)

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

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

8×	`sum3-define`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
6×	`--lowering--.f32`
6×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	24
1	5	24
2	7	24
3	8	24
4	10	24
5	16	24
6	20	24
7	26	24
8	29	24
0	29	24

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

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

Outputs
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)

eval6.0ms (0.2%)

Compiler: Compiled 799 to 103 computations (87.1% saved)

prune8.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	68	4	72

Accuracy

100.0%

Counts

72 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) x)
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
✓	55.7%	(*.f64 x x)
✓	46.4%	(neg.f64 x)

Compiler

Compiled 38 to 20 computations (47.4% saved)

regimes27.0ms (0.8%)

Counts

5 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(-.f64 (*.f64 x x) x)

Outputs
(-.f64 (*.f64 x x) x)

Calls

2 calls:

24.0ms	(*.f64 x (-.f64 x #s(literal 1 binary64)))
2.0ms	x

Results

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes4.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(-.f64 #s(literal 0 binary64) x)
(*.f64 x (-.f64 x #s(literal 1 binary64)))

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes2.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(-.f64 #s(literal 0 binary64) x)

Outputs
(*.f64 x x)
(neg.f64 x)
(*.f64 x x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.4%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(neg.f64 x)

Outputs
(neg.f64 x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
46.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch40.0ms (1.2%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
28.0ms	2.2739050884103616e-7	1.9151757556960365
11.0ms	-106568575.04021883	-7.888489314533524e-6

Results

27.0ms

304×

valid

Compiler

Compiled 181 to 121 computations (33.1% saved)

Precisions

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

ival-sub: 2.0ms (43.3% of total)

ival-mult: 2.0ms (43.3% of total)

const: 0.0ms (0% of total)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	24	26
2	30	26
3	36	26

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(-.f64 (*.f64 x x) x)
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(if (<=.f64 x #s(literal -1 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 1 binary64)) (neg.f64 x) (.f64 x x)))
(if (<=.f64 x #s(literal -1 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x) (.f64 x x)))
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)

soundness1.1s (33.7%)

Rules

3864×	`/-lowering-/.f32`
3864×	`/-lowering-/.f64`
2498×	`-lowering-.f32`
2498×	`-lowering-.f64`
1786×	`fnmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	23	8
2	140	7
3	1310	7
0	8675	7
0	5	9
1	34	9
2	284	9
3	4001	9
0	8058	9
0	15	83
1	33	83
2	76	83
3	151	74
4	451	74
5	1998	74
6	4524	74
7	7333	74
0	8125	74

Stop Event

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

Compiler

Compiled 55 to 28 computations (49.1% saved)

preprocess36.0ms (1.1%)

Compiler: Compiled 86 to 40 computations (53.5% saved)

Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2

analyze2.0ms (0.1%)

sample519.0ms (15.4%)

preprocess44.0ms (1.3%)

explain44.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify20.0ms (0.6%)

localize18.0ms (0.5%)

series1.0ms (0%)

rewrite304.0ms (9%)

simplify201.0ms (6%)

eval84.0ms (2.5%)

prune68.0ms (2%)

simplify36.0ms (1.1%)

localize29.0ms (0.9%)

series1.0ms (0%)

rewrite225.0ms (6.7%)

simplify221.0ms (6.6%)

eval70.0ms (2.1%)

prune48.0ms (1.4%)

simplify4.0ms (0.1%)

localize12.0ms (0.4%)

series0.0ms (0%)

rewrite123.0ms (3.6%)

simplify19.0ms (0.6%)

eval6.0ms (0.2%)

prune8.0ms (0.2%)

regimes27.0ms (0.8%)

regimes4.0ms (0.1%)

regimes2.0ms (0.1%)

regimes1.0ms (0%)

bsearch40.0ms (1.2%)

simplify7.0ms (0.2%)

soundness1.1s (33.7%)

preprocess36.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	5	16
1	10	16
2	18	16
3	41	16
4	79	16
5	125	16
6	373	16
7	549	16
8	700	16
9	788	16
10	796	16
0	796	16

Iter	Nodes	Cost
0	5	16
1	10	16
2	18	16
3	41	16
4	79	16
5	125	16
6	373	16
7	549	16
8	700	16
9	788	16
10	796	16
0	796	16

Iter	Nodes	Cost
0	5	16
1	10	16
2	18	16
3	41	16
4	79	16
5	125	16
6	373	16
7	549	16
8	700	16
9	788	16
10	796	16
0	796	16