Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 13 to 8 computations (38.5% saved)

sample647.0ms (70.3%)

Results

637.0ms

8256×

body

256

valid

Bogosity

preprocess14.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

9×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	8	5
2	13	5
3	19	5
4	23	5
5	33	5
6	35	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify9.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	8	5
2	13	5
3	19	5
4	23	5
5	33	5
6	35	5

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 10 to 4 computations (60% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(fma.f64 x x x)
▶	0.0b	(+.f64 x (*.f64 x x))

Compiler

Compiled 11 to 5 computations (54.5% saved)

localize4.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 x x))

Compiler

Compiled 10 to 3 computations (70% saved)

series5.0ms (0.5%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 x (*.f64 x x))
0.0ms	x	@	0	(+.f64 x (*.f64 x x))
0.0ms	x	@	-inf	(+.f64 x (*.f64 x x))

Compiler

Compiled 350 to 245 computations (30% saved)

rewrite38.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

502×	`pow1_binary64`
488×	`add-sqr-sqrt_binary64`
474×	`add-log-exp_binary64`
473×	`log1p-expm1-u_binary64`
473×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	92	5
2	1386	5

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x x))) (/.f64 (pow.f64 x 4) (-.f64 x (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x x)) (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2) (cbrt.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (/.f64 1 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) (pow.f64 x 4)) (/.f64 1 (-.f64 x (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 x 1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 x 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 x 1) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))) (+.f64 (pow.f64 x 3) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (.f64 x x)) (-.f64 (.f64 x x) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (pow.f64 x 4)) (-.f64 x (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 x 4))) (neg.f64 (-.f64 x (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 x x)) (-.f64 (.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 x x))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 x x))) (/.f64 (pow.f64 x 4) (-.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x x)) (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2) (cbrt.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (/.f64 1 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)) (/.f64 1 (-.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))) (+.f64 (pow.f64 x 3) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (*.f64 x x)) (-.f64 (*.f64 x x) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 x 4)) (-.f64 x (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 x 4))) (neg.f64 (-.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (-.f64 (*.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 x x))))))

simplify42.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-neg_binary64`
564×	`log-prod_binary64`
498×	`associate-l_binary64`
444×	`associate-r_binary64`
421×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	380
1	225	365
2	710	359
3	4659	359

Stop Event

1×	node limit

Counts

50 → 47

Calls

Call 1

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

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

localize3.0ms (0.3%)

Compiler: Compiled 6 to 2 computations (66.7% saved)

eval9.0ms (1%)

Compiler: Compiled 450 to 219 computations (51.3% saved)

prune6.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	46	3	49

Error

Counts

49 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (*.f64 x x))
▶	0.0b	(*.f64 (+.f64 x 1) x)
	1.6b	x

Compiler

Compiled 14 to 8 computations (42.9% saved)

localize4.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)

Compiler

Compiled 11 to 7 computations (36.4% saved)

series6.0ms (0.6%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (+.f64 x 1) x)
0.0ms	x	@	-inf	(*.f64 (+.f64 x 1) x)
0.0ms	x	@	inf	(*.f64 (+.f64 x 1) x)

Compiler

Compiled 350 to 245 computations (30% saved)

rewrite36.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

502×	`pow1_binary64`
487×	`add-sqr-sqrt_binary64`
468×	`log1p-expm1-u_binary64`
468×	`expm1-log1p-u_binary64`
467×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	103	7
2	1303	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

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

Outputs

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

simplify37.0ms (4%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
524×	`distribute-rgt-out_binary64`
476×	`fma-neg_binary64`
266×	`*-commutative_binary64`
264×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	180
1	136	172
2	371	166
3	2038	166
4	5058	166

Stop Event

1×	node limit

Counts

29 → 29

Calls

Call 1

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

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

eval5.0ms (0.5%)

Compiler: Compiled 223 to 116 computations (48% saved)

prune4.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	29	3	32

Error

Counts

32 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (*.f64 x x))
✓	0.0b	(*.f64 (+.f64 x 1) x)
	1.6b	x

Compiler

Compiled 14 to 8 computations (42.9% saved)

eval0.0ms (0%)

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

prune2.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (*.f64 x x))
✓	0.0b	(*.f64 (+.f64 x 1) x)
	1.6b	x

Compiler

Compiled 14 to 8 computations (42.9% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (*.f64 x x))
✓	0.0b	(*.f64 (+.f64 x 1) x)
	1.6b	x

Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes6.0ms (0.7%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(fma.f64 x x x)

Calls

2 calls:

3.0ms	(+.f64 x (*.f64 x x))
3.0ms	x

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`(+.f64 x (*.f64 x x))`

Compiler

Compiled 24 to 11 computations (54.2% saved)

regimes7.0ms (0.8%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
3.0ms	(+.f64 x (*.f64 x x))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(+.f64 x (*.f64 x x))`

Compiler

Compiled 20 to 10 computations (50% saved)

regimes3.0ms (0.3%)

Accuracy

Total -1.5b remaining (-3868%)

Threshold costs -1.5b (-3868%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 (+.f64 x 1) x)

Calls

1 calls:

2.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	13	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Outputs
(fma.f64 x x x)
(+.f64 x (*.f64 x x))
(*.f64 (+.f64 x 1) x)
(*.f64 x (+.f64 x 1))
x

Compiler

Compiled 19 to 10 computations (47.4% saved)

soundness8.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	8	5
2	13	5
3	19	5
4	23	5
5	33	5
6	35	5

Stop Event

1×

saturated

Compiler

Compiled 17 to 8 computations (52.9% saved)

end20.0ms (2.2%)

Compiler: Compiled 16 to 7 computations (56.3% saved)

Details

analyze0.0ms (0%)

sample647.0ms (70.3%)

preprocess14.0ms (1.5%)

simplify9.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize4.0ms (0.4%)

series5.0ms (0.5%)

rewrite38.0ms (4.1%)

simplify42.0ms (4.5%)

localize3.0ms (0.3%)

eval9.0ms (1%)

prune6.0ms (0.6%)

localize4.0ms (0.5%)

series6.0ms (0.6%)

rewrite36.0ms (4%)

simplify37.0ms (4%)

eval5.0ms (0.5%)

prune4.0ms (0.4%)

eval0.0ms (0%)

prune2.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes6.0ms (0.7%)

regimes7.0ms (0.8%)

regimes3.0ms (0.3%)

simplify3.0ms (0.3%)

soundness8.0ms (0.9%)

end20.0ms (2.2%)

Profiling