Details

analyze3.0ms (0.3%)

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)

sample594.0ms (63.9%)

Results

582.0ms	8256×	body	256	valid
1.0ms	10×	body	256	infinite

Bogosity

preprocess25.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

210×	`fma-def_binary64`
78×	`fma-neg_binary64`
28×	`distribute-rgt-in_binary64`
21×	`sub-neg_binary64`
19×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	34	8
3	70	8
4	143	8
5	205	8
6	283	8
7	378	8
8	590	8
9	610	8
10	640	8
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))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify17.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

210×	`fma-def_binary64`
78×	`fma-neg_binary64`
28×	`distribute-rgt-in_binary64`
21×	`sub-neg_binary64`
19×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	34	8
3	70	8
4	143	8
5	205	8
6	283	8
7	378	8
8	590	8
9	610	8
10	640	8

Stop Event

1×

saturated

Counts

1 → 3

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))

eval1.0ms (0.1%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))

Compiler

Compiled 8 to 6 computations (25% saved)

localize7.0ms (0.8%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))

Compiler

Compiled 19 to 14 computations (26.3% saved)

series2.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 x (-.f64 1 (.f64 x 1/2)))
1.0ms	x	@	0	(.f64 x (-.f64 1 (.f64 x 1/2)))
1.0ms	x	@	-inf	(.f64 x (-.f64 1 (.f64 x 1/2)))

rewrite40.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`pow1_binary64`
664×	`add-log-exp_binary64`
664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
653×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	147	10
2	1791	10

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (.f64 x -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 x (.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (.f64 (.f64 x -1/2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (.f64 (pow.f64 x 3) 1/8)) x) (+.f64 1 (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (.f64 (.f64 x x) 1/4)) x) (+.f64 1 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (-.f64 1 (.f64 (pow.f64 x 3) 1/8))) (+.f64 1 (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (-.f64 1 (.f64 (.f64 x x) 1/4))) (+.f64 1 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (.f64 (.f64 x -1/2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (.f64 (.f64 x -1/2) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 x -1/2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (.f64 (.f64 x -1/2) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (.f64 (.f64 x -1/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (.f64 (.f64 x -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (.f64 (.f64 x -1/2) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (.f64 x -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 1 (.f64 x -1/2)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (.f64 (.f64 x -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (.f64 (.f64 x -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 (*.f64 x -1/2)) (log.f64 x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (*.f64 x -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 x (*.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x (*.f64 (*.f64 x -1/2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 (pow.f64 x 3) 1/8)) x) (+.f64 1 (+.f64 (*.f64 x 1/2) (*.f64 (*.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 (*.f64 x x) 1/4)) x) (+.f64 1 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (-.f64 1 (*.f64 (pow.f64 x 3) 1/8))) (+.f64 1 (+.f64 (*.f64 x 1/2) (*.f64 (*.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (-.f64 1 (*.f64 (*.f64 x x) 1/4))) (+.f64 1 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (*.f64 x -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 1 (*.f64 x -1/2)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (*.f64 (*.f64 x -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 (*.f64 x -1/2)) (log.f64 x)))))))

simplify40.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
382×	`*-commutative_binary64`
329×	`associate-l_binary64`
323×	`associate-/r/_binary64`
280×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	314
1	155	306
2	495	288
3	2571	278
4	5608	278

Stop Event

1×	node limit

Counts

31 → 34

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

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

eval8.0ms (0.8%)

Compiler: Compiled 375 to 264 computations (29.6% saved)

prune5.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Error

Counts

35 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
▶	40.9b	(.f64 x (.f64 x -1/2))
	21.1b	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize4.0ms (0.5%)

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

localize7.0ms (0.8%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.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
1.0ms	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))

rewrite40.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`pow1_binary64`
671×	`add-log-exp_binary64`
670×	`log1p-expm1-u_binary64`
670×	`expm1-log1p-u_binary64`
658×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	134	8
2	1828	8

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (.f64 x -1/2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (fma.f64 x -1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (.f64 x -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x (.f64 x -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x (.f64 x -1/2) x)) (pow.f64 (cbrt.f64 (fma.f64 x (.f64 x -1/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x (.f64 x -1/2) x)) 2) (cbrt.f64 (fma.f64 x (.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x (.f64 x -1/2) x)) (sqrt.f64 (fma.f64 x (.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (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)))))))) (#(struct:change #<rule egg-rr> (2) ((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)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x -1/2 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (fma.f64 x -1/2 1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (fma.f64 x -1/2 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (fma.f64 x -1/2 1) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (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))))))) (#(struct:change #<rule egg-rr> (2) ((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))))))) (#(struct:change #<rule egg-rr> (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))))))) (#(struct:change #<rule egg-rr> (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))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 x (.f64 x -1/2)) 2)) (-.f64 x (.f64 x (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (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)))))))) (#(struct:change #<rule egg-rr> (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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (.f64 x -1/2)) 2) (.f64 x x)) (-.f64 (.f64 x (.f64 x -1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (.f64 x -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (.f64 x -1/2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (.f64 x -1/2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (.f64 x -1/2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (.f64 x -1/2) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (.f64 x -1/2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 x -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x -1/2) x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 x (.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (.f64 x -1/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 x -1/2))) 2) (cbrt.f64 (.f64 x (.f64 x -1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 x (.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x (.f64 x -1/2))) (sqrt.f64 (.f64 x (.f64 x -1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 x (.f64 x -1/2)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (*.f64 x -1/2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (fma.f64 x -1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/2) x)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/2) x)) 2) (cbrt.f64 (fma.f64 x (*.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/2) x)) (sqrt.f64 (fma.f64 x (*.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (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)))))))) (#(struct:change #<rule egg-rr> (2) ((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)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x -1/2 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 x -1/2 1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 x -1/2 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 x -1/2 1) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (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))))))) (#(struct:change #<rule egg-rr> (2) ((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))))))) (#(struct:change #<rule egg-rr> (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))))))) (#(struct:change #<rule egg-rr> (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))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 x (*.f64 x -1/2)) 2)) (-.f64 x (*.f64 x (*.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (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)))))))) (#(struct:change #<rule egg-rr> (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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (*.f64 x -1/2)) 2) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x -1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x -1/2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/2) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -1/2) x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 x (*.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (*.f64 x -1/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -1/2))) 2) (cbrt.f64 (*.f64 x (*.f64 x -1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 x (*.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (*.f64 x -1/2))) (sqrt.f64 (*.f64 x (*.f64 x -1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 x (*.f64 x -1/2)))))))

simplify41.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
528×	`cancel-sign-sub-inv_binary64`
518×	`div-sub_binary64`
289×	`fma-def_binary64`
246×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	587
1	244	567
2	842	537
3	4123	522

Stop Event

1×	node limit

Counts

52 → 50

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

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

eval13.0ms (1.4%)

Compiler: Compiled 693 to 438 computations (36.8% saved)

prune6.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	50	4	54

Error

Counts

54 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	40.9b	(.f64 x (.f64 x -1/2))
	21.1b	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0.2%)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	40.9b	(.f64 x (.f64 x -1/2))
	21.1b	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0.2%)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	40.9b	(.f64 x (.f64 x -1/2))
	21.1b	x

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes8.0ms (0.9%)

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 1 (.f64 x 1/2)))

Calls

2 calls:

4.0ms	(.f64 x (-.f64 1 (.f64 x 1/2)))
3.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(.f64 x (-.f64 1 (.f64 x 1/2)))`

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes9.0ms (1%)

Accuracy

Total -59.1b remaining (-4086.7%)

Threshold costs -59.1b (-4086.7%)

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

Error	Segments	Branch
1.4b	3	`x`

Compiler

Compiled 9 to 5 computations (44.4% saved)

bsearch27.0ms (2.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
12.0ms	0.9081984397122428	383.16061361028414
15.0ms	-1759.4239417700708	-3.602910296186366e-7

Results

24.0ms

288×

body

256

valid

Compiler

Compiled 192 to 135 computations (29.7% saved)

simplify4.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	28	38
2	37	38
3	45	38
4	53	38
5	55	38
6	56	38

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.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
(.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))))
x

Compiler

Compiled 30 to 20 computations (33.3% saved)

soundness0.0ms (0%)

end22.0ms (2.4%)

Compiler: Compiled 28 to 18 computations (35.7% saved)

Details

analyze3.0ms (0.3%)

sample594.0ms (63.9%)

preprocess25.0ms (2.7%)

simplify17.0ms (1.8%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

localize7.0ms (0.8%)

series2.0ms (0.2%)

rewrite40.0ms (4.3%)

simplify40.0ms (4.4%)

eval8.0ms (0.8%)

prune5.0ms (0.6%)

localize4.0ms (0.5%)

localize7.0ms (0.8%)

series1.0ms (0.1%)

rewrite40.0ms (4.3%)

simplify41.0ms (4.4%)

eval13.0ms (1.4%)

prune6.0ms (0.7%)

eval0.0ms (0%)

prune2.0ms (0.2%)

eval0.0ms (0%)

prune2.0ms (0.2%)

regimes8.0ms (0.9%)

regimes9.0ms (1%)

bsearch27.0ms (2.9%)

simplify4.0ms (0.4%)

soundness0.0ms (0%)

end22.0ms (2.4%)

Profiling