Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
85.7%	75%	12.5%	0%	12.5%	0%	0%	5
92.3%	75%	6.2%	0%	18.7%	0%	0%	6
96%	75%	3.1%	0%	21.9%	0%	0%	7
98%	75%	1.6%	0%	23.4%	0%	0%	8
99%	75%	0.8%	0%	24.2%	0%	0%	9
99.5%	75%	0.4%	0%	24.6%	0%	0%	10
99.7%	75%	0.2%	0%	24.8%	0%	0%	11
99.9%	75%	0.1%	0%	24.9%	0%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample623.0ms (43.9%)

Results

612.0ms	8256×	body	256	valid
1.0ms	14×	body	256	infinite

Bogosity

preprocess31.0ms (2.2%)

Algorithm

2×	egg-herbie

Rules

250×	`fma-def`
122×	`associate-r`
114×	`associate-+r+`
114×	`associate-+l+`
88×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(.f64 x (-.f64 1 (.f64 x 1/2)))

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify28.0ms (2%)

Algorithm

1×	egg-herbie

Rules

250×	`fma-def`
122×	`associate-r`
114×	`associate-+r+`
114×	`associate-+l+`
88×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Stop Event

1×

saturated

Counts

1 → 5

Calls

Call 1

Inputs
(.f64 x (-.f64 1 (.f64 x 1/2)))

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

eval1.0ms (0.1%)

Compiler: Compiled 33 to 21 computations (36.4% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Accurracy

100.0%

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x (*.f64 x -1/2) x)
▶	100.0%	(.f64 x (-.f64 1 (.f64 x 1/2)))

Compiler

Compiled 15 to 10 computations (33.3% saved)

localize7.0ms (0.5%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(.f64 x (-.f64 1 (.f64 x 1/2)))

Compiler

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 x (-.f64 1 (.f64 x 1/2)))
0.0ms	x	@	0	(.f64 x (-.f64 1 (.f64 x 1/2)))
0.0ms	x	@	-inf	(.f64 x (-.f64 1 (.f64 x 1/2)))

rewrite50.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1646×	`add-sqr-sqrt`
1624×	`*-un-lft-identity`
1518×	`add-cube-cbrt`
1502×	`add-cbrt-cube`
160×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	167	19
2	2037	19

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(.f64 x (-.f64 1 (.f64 x 1/2)))

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

Outputs

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

simplify55.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1054×	`*-commutative`
836×	`fma-def`
796×	`associate-/l*`
710×	`associate-r`
688×	`associate-+r+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	607
1	156	587
2	444	551
3	2410	531
4	4499	531

Stop Event

1×	node limit

Counts

31 → 35

Calls

Call 1

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

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

localize5.0ms (0.4%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

eval7.0ms (0.5%)

Compiler: Compiled 377 to 262 computations (30.5% saved)

prune6.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	33	4	37

Accurracy

100.0%

Counts

37 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	100.0%	(.f64 x (-.f64 1 (.f64 x 1/2)))
▶	42.3%	(.f64 x (.f64 x -1/2))
	60.5%	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize4.0ms (0.3%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

localize7.0ms (0.5%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(+.f64 x (.f64 (.f64 x -1/2) x))

Compiler

Compiled 18 to 11 computations (38.9% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 x (.f64 (.f64 x -1/2) x))
0.0ms	x	@	inf	(+.f64 x (.f64 (.f64 x -1/2) x))
0.0ms	x	@	-inf	(+.f64 x (.f64 (.f64 x -1/2) x))

rewrite58.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1652×	`add-sqr-sqrt`
1630×	`*-un-lft-identity`
1530×	`add-cube-cbrt`
1516×	`add-cbrt-cube`
154×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	153	15
2	2033	15

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

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

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

Outputs

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

simplify62.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1120×	`associate-+r+`
880×	`associate-+l+`
590×	`associate-*r/`
568×	`associate-/l/`
442×	`associate-/r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1432
1	261	1392
2	1040	1248
3	4145	1248

Stop Event

1×	node limit

Counts

54 → 59

Calls

Call 1

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

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

eval14.0ms (1%)

Compiler: Compiled 804 to 502 computations (37.6% saved)

prune8.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	59	4	63

Accurracy

100.0%

Counts

63 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	100.0%	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	42.3%	(.f64 x (.f64 x -1/2))
	60.5%	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	100.0%	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	42.3%	(.f64 x (.f64 x -1/2))
	60.5%	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	100.0%	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	42.3%	(.f64 x (.f64 x -1/2))
	60.5%	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes11.0ms (0.7%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(fma.f64 x (*.f64 x -1/2) x)

Calls

2 calls:

5.0ms	(.f64 x (-.f64 1 (.f64 x 1/2)))
4.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 x (-.f64 1 (.f64 x 1/2)))`

Compiler

Compiled 37 to 23 computations (37.8% saved)

regimes108.0ms (7.6%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(+.f64 x (.f64 (.f64 x -1/2) x))

Calls

2 calls:

103.0ms	x
4.0ms	(.f64 x (-.f64 1 (.f64 x 1/2)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 x (-.f64 1 (.f64 x 1/2)))`

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes8.0ms (0.6%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(.f64 x (.f64 x -1/2))
(.f64 x (-.f64 1 (.f64 x 1/2)))

Outputs
(.f64 x (-.f64 1 (.f64 x 1/2)))

Calls

2 calls:

4.0ms	x
4.0ms	(.f64 x (-.f64 1 (.f64 x 1/2)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 x (-.f64 1 (.f64 x 1/2)))`

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes9.0ms (0.6%)

Accuracy

Total -59.3b remaining (-4100.2%)

Threshold costs -59.3b (-4100.2%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(.f64 x (.f64 x -1/2))

Outputs
(.f64 x (.f64 x -1/2))
x
(.f64 x (.f64 x -1/2))

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
97.7%	3	`x`

Compiler

Compiled 9 to 5 computations (44.4% saved)

bsearch212.0ms (14.9%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
197.0ms	1.4814263233654311e-5	486197.658893187
15.0ms	-7855127059.134935	-0.013397198374061461

Results

208.0ms

320×

body

256

valid

Compiler

Compiled 212 to 149 computations (29.7% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative`
12×	`+-commutative`
6×	`distribute-lft-neg-in`
6×	`neg-mul-1`
6×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	93
1	44	93
2	56	93
3	64	93
4	71	93
5	73	93
6	74	93

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x (*.f64 x -1/2) x)
(+.f64 x (.f64 (.f64 x -1/2) x))
(.f64 x (-.f64 1 (.f64 x 1/2)))
(if (<=.f64 x -2) (.f64 x (.f64 x -1/2)) (if (<=.f64 x 2) x (.f64 x (.f64 x -1/2))))
x

Outputs
(fma.f64 x (*.f64 x -1/2) x)
(+.f64 x (.f64 (.f64 x -1/2) x))
(+.f64 x (.f64 x (.f64 x -1/2)))
(.f64 x (-.f64 1 (.f64 x 1/2)))
(.f64 x (+.f64 1 (.f64 x -1/2)))
(if (<=.f64 x -2) (.f64 x (.f64 x -1/2)) (if (<=.f64 x 2) x (.f64 x (.f64 x -1/2))))
(if (or (<=.f64 x -2) (not (<=.f64 x 2))) (.f64 x (.f64 x -1/2)) x)
x

Compiler

Compiled 41 to 27 computations (34.1% saved)

soundness56.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

250×	`fma-def`
122×	`associate-r`
114×	`associate-+r+`
114×	`associate-+l+`
88×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Stop Event

1×

saturated

Compiler

Compiled 64 to 42 computations (34.4% saved)

end31.0ms (2.2%)

Compiler: Compiled 37 to 23 computations (37.8% saved)

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15
0	1	1

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15
0	1	1

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Details

analyze3.0ms (0.2%)

sample623.0ms (43.9%)

preprocess31.0ms (2.2%)

simplify28.0ms (2%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

localize7.0ms (0.5%)

series1.0ms (0.1%)

rewrite50.0ms (3.6%)

simplify55.0ms (3.9%)

localize5.0ms (0.4%)

eval7.0ms (0.5%)

prune6.0ms (0.4%)

localize4.0ms (0.3%)

localize7.0ms (0.5%)

series1.0ms (0.1%)

rewrite58.0ms (4.1%)

simplify62.0ms (4.4%)

eval14.0ms (1%)

prune8.0ms (0.6%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes11.0ms (0.7%)

regimes108.0ms (7.6%)

regimes8.0ms (0.6%)

regimes9.0ms (0.6%)

bsearch212.0ms (14.9%)

simplify8.0ms (0.5%)

soundness56.0ms (3.9%)

end31.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15
0	1	1

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15

Iter	Nodes	Cost
0	8	19
1	18	19
2	40	15
3	77	15
4	149	15
5	241	15
6	319	15
7	420	15
8	731	15
9	886	15
10	916	15