Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	50%	0%	0%	50%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
33.3%	12.5%	25%	0%	0%	62.5%	0%	4
60%	18.7%	12.5%	0%	0%	68.7%	0%	5
77.8%	21.9%	6.2%	0%	0%	71.8%	0%	6
88.2%	23.4%	3.1%	0%	0%	73.4%	0%	7
93.9%	24.2%	1.6%	0%	0%	74.2%	0%	8
96.9%	24.6%	0.8%	0%	0%	74.6%	0%	9
98.4%	24.8%	0.4%	0%	0%	74.8%	0%	10
99.2%	24.9%	0.2%	0%	0%	74.9%	0%	11
99.6%	24.9%	0.1%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample827.0ms (44.6%)

Results

814.0ms	8256×	body	256	valid
1.0ms	11×	body	256	invalid

Bogosity

preprocess16.0ms (0.9%)

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 (0.3%)

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)

prune1.0ms (0.1%)

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)

localize8.0ms (0.5%)

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)

series2.0ms (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))

rewrite49.0ms (2.6%)

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)))))))))

simplify115.0ms (6.2%)

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 (0.3%)

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

prune5.0ms (0.3%)

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

Counts

26 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(-.f64 x 1/2)
▶	29.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
▶	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
	1.6b	x

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 x -1))
✓	27.7b	(sqrt.f64 (*.f64 x (+.f64 x -1)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series3.0ms (0.1%)

Counts

2 → 20

Calls

6 calls:

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

rewrite136.0ms (7.3%)

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	16
1	129	16
2	1645	16

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

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

simplify60.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-neg_binary64`
616×	`times-frac_binary64`
572×	`cancel-sign-sub-inv_binary64`
501×	`associate-/r*_binary64`
349×	`associate-/l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	157
1	68	144
2	161	144
3	394	144
4	989	144
5	2803	144

Stop Event

1×	node limit

Counts

66 → 65

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

localize8.0ms (0.4%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

localize17.0ms (0.9%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 40 to 30 computations (25% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

881×	`pow1_binary64`
835×	`add-log-exp_binary64`
835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
822×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	163	10
2	2180	10

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (*.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (neg.f64 (/.f64 -1/16 x))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 -1/8 (/.f64 -1/16 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 -1/8 (/.f64 -1/16 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))

simplify61.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

505×	`distribute-neg-frac_binary64`
485×	`associate-/l*_binary64`
485×	`fma-neg_binary64`
434×	`unswap-sqr_binary64`
360×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	150
1	37	132
2	77	132
3	164	132
4	425	132
5	1467	132
6	4000	132
7	7470	132

Stop Event

1×	node limit

Counts

43 → 36

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))))

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

localize6.0ms (0.3%)

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

eval59.0ms (3.2%)

Compiler: Compiled 1206 to 871 computations (27.8% saved)

prune43.0ms (2.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(-.f64 x 1/2)
✓	29.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.6b	x
✓	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

eval0.0ms (0%)

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

prune4.0ms (0.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

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

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(-.f64 x 1/2)
✓	29.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.6b	x
✓	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

eval0.0ms (0%)

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

prune4.0ms (0.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

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

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(-.f64 x 1/2)
✓	29.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.6b	x
✓	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓	0.1b	(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

regimes27.0ms (1.4%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

13.0ms	x
11.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))`

Compiler

Compiled 47 to 32 computations (31.9% saved)

regimes10.0ms (0.5%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.1b	1	`x`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes9.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(-.f64 x 1/2)

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.6b	1	`x`

Compiler

Compiled 8 to 4 computations (50% saved)

regimes15.0ms (0.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
1.6b	1	`x`

Compiler

Compiled 5 to 2 computations (60% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	22	31
2	23	31

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

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

Compiler

Compiled 26 to 19 computations (26.9% saved)

soundness212.0ms (11.4%)

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)

end71.0ms (3.8%)

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

Details

analyze4.0ms (0.2%)

sample827.0ms (44.6%)

preprocess16.0ms (0.9%)

simplify6.0ms (0.3%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize8.0ms (0.5%)

series2.0ms (0.1%)

rewrite49.0ms (2.6%)

simplify115.0ms (6.2%)

eval6.0ms (0.3%)

prune5.0ms (0.3%)

localize7.0ms (0.4%)

series3.0ms (0.1%)

rewrite136.0ms (7.3%)

simplify60.0ms (3.3%)

localize8.0ms (0.4%)

localize17.0ms (0.9%)

series2.0ms (0.1%)

rewrite51.0ms (2.8%)

simplify61.0ms (3.3%)

localize6.0ms (0.3%)

eval59.0ms (3.2%)

prune43.0ms (2.3%)

eval0.0ms (0%)

prune4.0ms (0.2%)

eval0.0ms (0%)

prune4.0ms (0.2%)

regimes27.0ms (1.4%)

regimes10.0ms (0.5%)

regimes9.0ms (0.5%)

regimes15.0ms (0.8%)

simplify6.0ms (0.3%)

soundness212.0ms (11.4%)

end71.0ms (3.8%)

Profiling