Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	50%	50%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (52.4%)

Results

1.4s	8256×	body	256	valid
1.0ms	7×	body	256	invalid

preprocess14.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	14	11
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	14	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

prune80.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series3.0ms (0.1%)

Counts

1 → 8

Calls

3 calls:

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

rewrite53.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`pow1_binary64`
603×	`add-log-exp_binary64`
602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
587×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	146	9
2	1759	9

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

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

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

Outputs

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

simplify61.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

744×	`associate-/r/_binary64`
666×	`div-sub_binary64`
253×	`*-commutative_binary64`
240×	`fma-def_binary64`
234×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	68
1	88	68
2	244	68
3	677	64
4	3120	62
5	7186	62

Stop Event

1×	node limit

Counts

22 → 25

Calls

Call 1

Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))

Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1/16 x) 1/8)))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) -1/2))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
x
(+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 x -1/2)
(-.f64 x 1/2)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1/16 x) 1/8)))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) -1/2))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

eval6.0ms (0.2%)

Compiler: Compiled 254 to 206 computations (18.9% saved)

prune5.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	20	5	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	5	26

Error

0.0b

Counts

26 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.8b	(-.f64 x 1/2)
▶	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶	0.6b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
	1.6b	x
▶	0.5b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.7b	(sqrt.f64 (*.f64 x (+.f64 x -1)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

646×	`pow1_binary64`
602×	`add-log-exp_binary64`
602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
590×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	129	9
2	1645	9

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

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

Outputs

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

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

616×	`times-frac_binary64`
536×	`fma-neg_binary64`
520×	`div-sub_binary64`
498×	`associate-/r*_binary64`
479×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	74
1	65	70
2	150	70
3	365	70
4	883	70
5	2292	70
6	7688	70

Stop Event

1×	node limit

Counts

30 → 37

Calls

Call 1

Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (.f64 -1 x) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))

Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (-.f64 x 1/2) (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))))
(+.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x -1/2) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (.f64 -1 x) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 (/.f64 1/8 x) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) x)))
(-.f64 (-.f64 1/2 x) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

Compiler

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
0.0ms	x	@	-inf	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
0.0ms	x	@	inf	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

rewrite53.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

975×	`pow1_binary64`
921×	`add-log-exp_binary64`
921×	`log1p-expm1-u_binary64`
921×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	167	10
2	2377	10

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

Inputs
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))) (/.f64 (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2) (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 2) (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3)) (/.f64 1 (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2)) (/.f64 1 (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3)) (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3)) (+.f64 (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2)) (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2))) (neg.f64 (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x -1/2) 3) (/.f64 -1/512 (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (-.f64 (/.f64 1/64 (*.f64 x x)) (*.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2) (*.f64 x x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (+.f64 -1/2 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 -1/2 (/.f64 -1/8 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) 2) (cbrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 -1/2 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) (sqrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 -1/2 (/.f64 -1/8 x)))))))

simplify33.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

180×	`fma-neg_binary64`
110×	`fma-def_binary64`
47×	`cancel-sign-sub-inv_binary64`
36×	`associate-/l*_binary64`
33×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	83
1	29	81
2	60	81
3	104	81
4	190	81
5	278	81
6	463	81
7	615	81
8	693	81
9	765	81
10	837	81
11	857	81
12	875	81

Stop Event

1×

saturated

Counts

48 → 44

Calls

Call 1

Inputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))

Outputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

localize16.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.0b	(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)

Compiler

Compiled 40 to 30 computations (25% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
1.0ms	x	@	-inf	(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
0.0ms	x	@	inf	(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
0.0ms	x	@	0	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
0.0ms	x	@	-inf	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

rewrite72.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`prod-diff_binary64`
521×	`log-prod_binary64`
394×	`fma-def_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	242	26
2	3503	26

Stop Event

1×	node limit

Counts

2 → 108

Calls

Call 1

Inputs
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

Outputs

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x) 3)) (/.f64 1 (fma.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) (-.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 1/4)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1/4 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2)) (/.f64 1 (-.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x -1/2) 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 x -1/2)) (cbrt.f64 (+.f64 x -1/2))) (cbrt.f64 (+.f64 x -1/2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x -1/2)) (sqrt.f64 (+.f64 x -1/2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (cbrt.f64 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (cbrt.f64 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (sqrt.f64 x)) (+.f64 x -1/2))))))

simplify61.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
496×	`cancel-sign-sub-inv_binary64`
484×	`associate-/l*_binary64`
457×	`unswap-sqr_binary64`
411×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	277
1	59	255
2	150	255
3	356	255
4	887	255
5	2555	255
6	6344	255

Stop Event

1×	node limit

Counts

132 → 122

Calls

Call 1

Inputs
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))

Outputs
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x)))
(neg.f64 (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2)
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2)))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (-.f64 (/.f64 -1/8 x) 1/2))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2)))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (-.f64 (/.f64 -1/8 x) 1/2))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2)))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) 1/2) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (*.f64 (/.f64 -1 x) (-.f64 1/8 (/.f64 -1/16 x))) -1/2))

localize3.0ms (0.1%)

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

eval72.0ms (2.5%)

Compiler: Compiled 3207 to 2424 computations (24.4% saved)

prune26.0ms (0.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	202	6	208

Error

Counts

208 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶	31.3b	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
✓	0.5b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.6b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
	1.6b	x

Compiler

Compiled 55 to 40 computations (27.3% saved)

localize24.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1/64 (*.f64 x x))
✓	28.7b	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))

Compiler

Compiled 67 to 43 computations (35.8% saved)

series90.0ms (3.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
86.0ms	x	@	inf	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
1.0ms	x	@	0	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
1.0ms	x	@	-inf	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
1.0ms	x	@	0	(/.f64 1/64 (*.f64 x x))
0.0ms	x	@	inf	(/.f64 1/64 (*.f64 x x))

rewrite100.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`fma-def_binary64`
323×	`fma-neg_binary64`
313×	`log-div_binary64`
237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	323	17
2	5361	17

Stop Event

1×	node limit

Counts

2 → 230

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(/.f64 1/64 (*.f64 x x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (/.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (fma.f64 (neg.f64 (/.f64 1 x)) -1/8 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (fma.f64 (neg.f64 (/.f64 -1/2 (cbrt.f64 x))) (*.f64 1/4 (cbrt.f64 (pow.f64 x -2))) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (+.f64 (/.f64 -1/8 x) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (+.f64 x -1/2) 2) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (neg.f64 (*.f64 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simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-neg_binary64`
527×	`associate-/l*_binary64`
504×	`div-sub_binary64`
474×	`fma-def_binary64`
457×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	167
1	37	165
2	74	165
3	143	165
4	322	165
5	831	165
6	2762	165
7	6531	165

Stop Event

1×	node limit

Counts

254 → 239

Calls

Call 1

Inputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))

Outputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))

eval123.0ms (4.2%)

Compiler: Compiled 5510 to 4294 computations (22.1% saved)

prune33.0ms (1.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	0	1
Picked	0	1	1
Done	0	4	4
Total	239	6	245

Error

Counts

245 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓	31.3b	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
✓	0.5b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.6b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
	1.6b	x

Compiler

Compiled 55 to 40 computations (27.3% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

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

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓	31.3b	(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
✓	0.5b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.6b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
	1.6b	x

Compiler

Compiled 55 to 40 computations (27.3% saved)

regimes14.0ms (0.5%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (-.f64 (.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x 1/2)
x
x
x

Outputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

Calls

2 calls:

6.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
5.0ms	x

Results

Error	Segments	Branch
0.5b	1	`x`
0.5b	1	`(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))`

Compiler

Compiled 69 to 47 computations (31.9% saved)

regimes6.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x 1/2)
x
x
x

Outputs
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
0.6b	1	`x`

Compiler

Compiled 16 to 9 computations (43.8% saved)

regimes5.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(-.f64 x 1/2)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.8b	1	`x`

Compiler

Compiled 9 to 4 computations (55.6% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs
x
x
x

Outputs
x

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
1.6b	1	`x`

Compiler

Compiled 6 to 2 computations (66.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	22	32
2	23	32

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x 1/2)
x
x

Outputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x 1/2)
(+.f64 x -1/2)
x
x

Compiler

Compiled 26 to 19 computations (26.9% saved)

soundness166.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

744×	`associate-/r/_binary64`
666×	`div-sub_binary64`
253×	`*-commutative_binary64`
240×	`fma-def_binary64`
234×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	68
1	88	68
2	244	68
3	677	64
4	3120	62
5	7186	62

Stop Event

1×	node limit

Compiler

Compiled 660 to 564 computations (14.5% saved)

end50.0ms (1.7%)

Compiler: Compiled 23 to 16 computations (30.4% saved)

Iter	Nodes	Cost
0	13	83
1	29	81
2	60	81
3	104	81
4	190	81
5	278	81
6	463	81
7	615	81
8	693	81
9	765	81
10	837	81
11	857	81
12	875	81

Iter	Nodes	Cost
0	13	83
1	29	81
2	60	81
3	104	81
4	190	81
5	278	81
6	463	81
7	615	81
8	693	81
9	765	81
10	837	81
11	857	81
12	875	81

Details

analyze3.0ms (0.1%)

sample1.5s (52.4%)

preprocess14.0ms (0.5%)

simplify6.0ms (0.2%)

eval1.0ms (0%)

prune80.0ms (2.7%)

localize9.0ms (0.3%)

series3.0ms (0.1%)

rewrite53.0ms (1.8%)

simplify61.0ms (2.1%)

eval6.0ms (0.2%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

series1.0ms (0%)

rewrite42.0ms (1.4%)

simplify65.0ms (2.2%)

localize8.0ms (0.3%)

series1.0ms (0%)

rewrite53.0ms (1.8%)

simplify33.0ms (1.1%)

localize16.0ms (0.6%)

series3.0ms (0.1%)

rewrite72.0ms (2.5%)

simplify61.0ms (2.1%)

localize3.0ms (0.1%)

eval72.0ms (2.5%)

prune26.0ms (0.9%)

localize24.0ms (0.8%)

series90.0ms (3.1%)

rewrite100.0ms (3.4%)

simplify64.0ms (2.2%)

eval123.0ms (4.2%)

prune33.0ms (1.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes14.0ms (0.5%)

regimes6.0ms (0.2%)

regimes5.0ms (0.2%)

regimes4.0ms (0.1%)

simplify4.0ms (0.1%)

soundness166.0ms (5.7%)

end50.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	13	83
1	29	81
2	60	81
3	104	81
4	190	81
5	278	81
6	463	81
7	615	81
8	693	81
9	765	81
10	837	81
11	857	81
12	875	81