Metrics for Expanding a square

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 11 to 9 computations (18.2% saved)

sample833.0ms (42.5%)

Results

278.0ms	2045×	body	1024	valid
220.0ms	2907×	body	256	valid
180.0ms	2042×	body	256	infinite
111.0ms	1062×	body	512	valid
33.0ms	200×	body	2048	valid

Bogosity

preprocess236.0ms (12%)

Algorithm

1×	egg-herbie

Rules

5558×	`fma-neg`
2282×	`unsub-neg`
820×	`distribute-neg-in`
702×	`sub-neg`
576×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	43	40
2	118	30
3	365	26
4	1816	26
5	3230	26
6	4275	26
7	5101	26
8	5607	26
9	5857	26
10	5859	26
11	5859	26
12	5975	26
13	6030	26
14	6033	26
15	6033	26

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(-.f64 (*.f64 (+.f64 (neg.f64 x) 1) (+.f64 (neg.f64 x) 1)) 1)

Outputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(fma.f64 (+.f64 x 1) (+.f64 x 1) -1)
(*.f64 (+.f64 x 2) (+.f64 x 0))
(*.f64 x (+.f64 x 2))
(-.f64 (*.f64 (+.f64 (neg.f64 x) 1) (+.f64 (neg.f64 x) 1)) 1)
(fma.f64 (+.f64 1 (neg.f64 x)) (+.f64 1 (neg.f64 x)) -1)
(fma.f64 (-.f64 1 x) (-.f64 1 x) -1)
(*.f64 (neg.f64 x) (-.f64 2 x))
(*.f64 x (+.f64 x -2))

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify61.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1906×	`fma-def`
1604×	`fma-neg`
1178×	`distribute-lft-in`
1078×	`associate--r-`
1078×	`distribute-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	25	19
2	58	13
3	138	13
4	583	13
5	2037	13
6	5456	13
7	7831	13

Stop Event

1×	node limit

Counts

1 → 5

Calls

Call 1

Inputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

Outputs
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
(fma.f64 (+.f64 x 1) (+.f64 x 1) -1)
(*.f64 (+.f64 x 2) (+.f64 x 0))
(*.f64 x (+.f64 x 2))
(*.f64 x (-.f64 x -2))

eval1.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	4	1	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	1	6

Accurracy

100.0%

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 x (-.f64 x -2))
▶	100.0%	(*.f64 x (-.f64 x -2))

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize19.0ms (1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(*.f64 x (-.f64 x -2))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(*.f64 x (-.f64 x -2))
0.0ms	x	@	inf	(*.f64 x (-.f64 x -2))
0.0ms	x	@	0	(*.f64 x (-.f64 x -2))

rewrite50.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1366×	`pow1`
1274×	`add-exp-log`
1274×	`log1p-expm1-u`
1274×	`expm1-log1p-u`
1252×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	133	13
2	1674	13

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(*.f64 x (-.f64 x -2))

Outputs
(+.f64 (.f64 x x) (.f64 x 2))
(+.f64 (.f64 x x) (.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))

simplify52.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1670×	`fma-def`
1268×	`log-prod`
724×	`*-commutative`
646×	`distribute-lft-out`
640×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	451
1	134	443
2	398	435
3	2440	431
4	5933	431

Stop Event

1×	node limit

Counts

29 → 29

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 x 2))
(+.f64 (.f64 x x) (.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))

Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 x x) (.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (.f64 x x) (.f64 2 x))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(/.f64 (.f64 x (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 x (/.f64 (fma.f64 x x (+.f64 4 (*.f64 x -2))) (+.f64 (pow.f64 x 3) 8)))
(/.f64 x (/.f64 (fma.f64 x x (fma.f64 x -2 4)) (+.f64 (pow.f64 x 3) 8)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x x (fma.f64 x -2 4)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(*.f64 (/.f64 x (+.f64 x -2)) (fma.f64 x x -4))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) 8) x) (fma.f64 x x (+.f64 4 (.f64 x -2))))
(/.f64 x (/.f64 (fma.f64 x x (+.f64 4 (*.f64 x -2))) (+.f64 (pow.f64 x 3) 8)))
(/.f64 x (/.f64 (fma.f64 x x (fma.f64 x -2 4)) (+.f64 (pow.f64 x 3) 8)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x x (fma.f64 x -2 4)))
(/.f64 (fma.f64 x 8 (pow.f64 x 4)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (*.f64 (fma.f64 x x -4) x) (+.f64 x -2))
(/.f64 (*.f64 x (fma.f64 x x -4)) (+.f64 x -2))
(*.f64 (/.f64 x (+.f64 x -2)) (fma.f64 x x -4))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(*.f64 x (+.f64 2 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(*.f64 x (+.f64 2 x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(*.f64 x (+.f64 2 x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(*.f64 x (+.f64 2 x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))

eval5.0ms (0.3%)

Compiler: Compiled 254 to 169 computations (33.5% saved)

prune5.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	4	30

Accurracy

100.0%

Counts

30 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 x x) (.f64 x 2))
▶	47.6%	(+.f64 x x)
✓	100.0%	(*.f64 x (-.f64 x -2))
▶	54.9%	(*.f64 x x)
▶	100.0%	(+.f64 (.f64 x x) (.f64 x 2))
▶	47.6%	(+.f64 x x)
✓	100.0%	(*.f64 x (-.f64 x -2))
▶	54.9%	(*.f64 x x)

Compiler

Compiled 44 to 26 computations (40.9% saved)

localize34.0ms (1.7%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 x 2))

Compiler

Compiled 25 to 10 computations (60% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (.f64 x x) (.f64 x 2))
0.0ms	x	@	-inf	(+.f64 (.f64 x x) (.f64 x 2))
0.0ms	x	@	inf	(+.f64 (.f64 x x) (.f64 x 2))

rewrite52.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1580×	`pow1`
1474×	`add-exp-log`
1472×	`log1p-expm1-u`
1472×	`expm1-log1p-u`
1448×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	154	13
2	2056	13

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 x 2))

Outputs
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(-.f64 (/.f64 (pow.f64 x 4) (.f64 x (-.f64 x 2))) (/.f64 (.f64 (.f64 x x) 4) (.f64 x (-.f64 x 2))))
(*.f64 x (+.f64 x 2))
(.f64 (.f64 x (+.f64 x 2)) 1)
(.f64 1 (.f64 x (+.f64 x 2)))
(.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x 2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x 2)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))))
(.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (/.f64 1 (.f64 x (-.f64 x 2))))
(*.f64 (+.f64 x 2) x)
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2))) (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6))))
(/.f64 1 (/.f64 (.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (.f64 (*.f64 x x) 4))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 (pow.f64 x 3) 2))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (*.f64 x (-.f64 x 2)))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (-.f64 (.f64 x 2) (.f64 x x)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (exp.f64 (*.f64 x (+.f64 x 2))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(fma.f64 x x (*.f64 x 2))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))
(fma.f64 1 (.f64 x x) (.f64 x 2))
(fma.f64 1 (.f64 x 2) (.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 2)) 2) (cbrt.f64 (.f64 x 2)) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))
(fma.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2)) (*.f64 x x))

simplify54.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-neg`
928×	`div-sub`
820×	`times-frac`
632×	`fma-def`
580×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1157
1	284	1107
2	995	981
3	5227	981

Stop Event

1×	node limit

Counts

51 → 55

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(-.f64 (/.f64 (pow.f64 x 4) (.f64 x (-.f64 x 2))) (/.f64 (.f64 (.f64 x x) 4) (.f64 x (-.f64 x 2))))
(*.f64 x (+.f64 x 2))
(.f64 (.f64 x (+.f64 x 2)) 1)
(.f64 1 (.f64 x (+.f64 x 2)))
(.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x 2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x 2)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))))
(.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (/.f64 1 (.f64 x (-.f64 x 2))))
(*.f64 (+.f64 x 2) x)
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2))) (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6))))
(/.f64 1 (/.f64 (.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (.f64 (*.f64 x x) 4))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 (pow.f64 x 3) 2))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (*.f64 x (-.f64 x 2)))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (-.f64 (.f64 x 2) (.f64 x x)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(log.f64 (exp.f64 (*.f64 x (+.f64 x 2))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(fma.f64 x x (*.f64 x 2))
(fma.f64 x 2 (*.f64 x x))
(fma.f64 2 x (*.f64 x x))
(fma.f64 1 (.f64 x x) (.f64 x 2))
(fma.f64 1 (.f64 x 2) (.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 2)) 2) (cbrt.f64 (.f64 x 2)) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))
(fma.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2)) (*.f64 x x))

Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)
(*.f64 x (+.f64 2 x))
(-.f64 (/.f64 (pow.f64 x 4) (.f64 x (-.f64 x 2))) (/.f64 (.f64 (.f64 x x) 4) (.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) 4)) (.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(.f64 (.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(.f64 1 (.f64 x (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))
(*.f64 x (+.f64 2 x))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x 2)))
(*.f64 x (+.f64 2 x))
(.f64 (sqrt.f64 (.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 x (.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (.f64 x x) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (/.f64 1 (.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) 4)) (.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(*.f64 (+.f64 x 2) x)
(*.f64 x (+.f64 2 x))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2))) (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 x (.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (.f64 x x) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 1 (/.f64 (.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (.f64 (*.f64 x x) 4))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) 4)) (.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 x (.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (.f64 x x) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6)) (+.f64 (.f64 (.f64 x x) 4) (-.f64 (pow.f64 x 4) (.f64 (pow.f64 x 3) 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 x (.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (.f64 x x) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (*.f64 x (-.f64 x 2)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) 4)) (.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 3) 2)))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (.f64 x (.f64 x 4)) (*.f64 2 (pow.f64 x 3)))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 x (.f64 x 4) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (fma.f64 4 (.f64 x x) (.f64 (pow.f64 x 3) (+.f64 x -2))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) 4)) (.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(/.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (-.f64 (.f64 x 2) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 x (.f64 x 4))) (*.f64 x (+.f64 x -2)))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) 4)) (.f64 x (+.f64 x -2)))
(*.f64 x (/.f64 (fma.f64 x x -4) (+.f64 x -2)))
(pow.f64 (*.f64 x (+.f64 x 2)) 1)
(*.f64 x (+.f64 2 x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)
(*.f64 x (+.f64 2 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)
(*.f64 x (+.f64 2 x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 2)
(*.f64 x (+.f64 2 x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))
(*.f64 x (+.f64 2 x))
(log.f64 (exp.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))
(*.f64 x (+.f64 2 x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))
(*.f64 x (+.f64 2 x))
(fma.f64 x x (*.f64 x 2))
(*.f64 x (+.f64 2 x))
(fma.f64 x 2 (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 1 (.f64 x x) (.f64 x 2))
(*.f64 x (+.f64 2 x))
(fma.f64 1 (.f64 x 2) (.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 2)) 2) (cbrt.f64 (.f64 x 2)) (*.f64 x x))
(*.f64 x (+.f64 2 x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 2 x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (*.f64 2 x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (+.f64 x x))
(fma.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2)) (*.f64 x x))
(*.f64 x (+.f64 2 x))

eval12.0ms (0.6%)

Compiler: Compiled 671 to 447 computations (33.4% saved)

prune7.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	55	4	59

Accurracy

100.0%

Counts

59 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 x 2))
✓	47.6%	(+.f64 x x)
✓	100.0%	(*.f64 x (-.f64 x -2))
✓	54.9%	(*.f64 x x)

Compiler

Compiled 50 to 29 computations (42% saved)

regimes12.0ms (0.6%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)
(*.f64 x (-.f64 x -2))
(+.f64 (.f64 x x) (.f64 x 2))
(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)

Outputs
(*.f64 x (-.f64 x -2))

Calls

4 calls:

4.0ms	x
3.0ms	(+.f64 x 1)
2.0ms	(-.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) 1)
2.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

Results

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

Compiler

Compiled 52 to 34 computations (34.6% saved)

regimes67.0ms (3.4%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)

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

Calls

1 calls:

66.0ms

Results

Accuracy	Segments	Branch
97.7%	3	`x`

Compiler

Compiled 9 to 4 computations (55.6% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
54.9%	1	`x`

Compiler

Compiled 6 to 3 computations (50% saved)

bsearch26.0ms (1.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.7176267404345593	50975563.3018649
13.0ms	-1911.365530602927	-3.4697932031732214e-6

Results

23.0ms

288×

body

256

valid

Compiler

Compiled 194 to 119 computations (38.7% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg`
4×	`+-commutative`
4×	`*-commutative`
2×	`neg-mul-1`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
1	25	59
2	30	59
3	32	59
4	33	59

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 x (-.f64 x -2))
(if (<=.f64 x -2) (.f64 x x) (if (<=.f64 x 2) (+.f64 x x) (.f64 x x)))
(*.f64 x x)

Outputs
(*.f64 x (-.f64 x -2))
(if (<=.f64 x -2) (.f64 x x) (if (<=.f64 x 2) (+.f64 x x) (.f64 x x)))
(*.f64 x x)

Compiler

Compiled 28 to 15 computations (46.4% saved)

soundness282.0ms (14.4%)

Rules

1906×	`fma-def`
1670×	`fma-def`
1670×	`fma-def`
1604×	`fma-neg`
1268×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	25	19
2	58	13
3	138	13
4	583	13
5	2037	13
6	5456	13
7	7831	13
0	58	451
1	134	443
2	398	435
3	2440	431
4	5933	431
0	58	451
1	134	443
2	398	435
3	2440	431
4	5933	431

Stop Event

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

Compiler

Compiled 150 to 112 computations (25.3% saved)

end140.0ms (7.2%)

Compiler: Compiled 72 to 40 computations (44.4% saved)

analyze0.0ms (0%)

sample833.0ms (42.5%)

preprocess236.0ms (12%)

simplify61.0ms (3.1%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize19.0ms (1%)

series1.0ms (0.1%)

rewrite50.0ms (2.6%)

simplify52.0ms (2.7%)

eval5.0ms (0.3%)

prune5.0ms (0.3%)

localize34.0ms (1.7%)

series1.0ms (0%)

rewrite52.0ms (2.7%)

simplify54.0ms (2.7%)

eval12.0ms (0.6%)

prune7.0ms (0.4%)

regimes12.0ms (0.6%)

regimes67.0ms (3.4%)

regimes3.0ms (0.1%)

bsearch26.0ms (1.4%)

simplify5.0ms (0.2%)

soundness282.0ms (14.4%)

end140.0ms (7.2%)

Profiling