Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample766.0ms (55.1%)

Results

754.0ms	8256×	body	256	valid
1.0ms	11×	body	256	infinite

Bogosity

preprocess28.0ms (2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify18.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% 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

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 8 to 6 computations (25% saved)

localize8.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

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

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

Outputs

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

simplify136.0ms (9.8%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-def_binary64`
778×	`sqr-pow_binary64`
502×	`cube-prod_binary64`
484×	`associate-l_binary64`
476×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	87
1	15	87
2	27	87
3	54	87
4	134	87
5	426	87
6	1599	87
7	3011	87
8	3373	87
9	3604	87
10	3847	87
11	4196	87
12	4620	87
13	5152	87
14	5737	87
15	6459	87
16	7298	87
17	7696	87
18	7982	87

Stop Event

1×	node limit

Counts

31 → 24

Calls

Call 1

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

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

eval6.0ms (0.4%)

Compiler: Compiled 241 to 170 computations (29.5% saved)

prune4.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Error

Counts

25 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	41.5b	(.f64 x (.f64 x -1/2))
	20.6b	x
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
▶	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize5.0ms (0.3%)

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

localize7.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 11 computations (38.9% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

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

Outputs

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

simplify142.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-def_binary64`
778×	`sqr-pow_binary64`
502×	`cube-prod_binary64`
484×	`associate-l_binary64`
476×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	87
1	15	87
2	27	87
3	54	87
4	134	87
5	426	87
6	1599	87
7	3011	87
8	3373	87
9	3604	87
10	3847	87
11	4196	87
12	4620	87
13	5152	87
14	5737	87
15	6459	87
16	7298	87
17	7696	87
18	7982	87

Stop Event

1×	node limit

Counts

52 → 44

Calls

Call 1

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

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

eval12.0ms (0.9%)

Compiler: Compiled 579 to 367 computations (36.6% saved)

prune7.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	44	4	48

Error

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.5b	(.f64 x (.f64 x -1/2))
	20.6b	x
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))

Compiler

Compiled 24 to 16 computations (33.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.5b	(.f64 x (.f64 x -1/2))
	20.6b	x
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))

Compiler

Compiled 24 to 16 computations (33.3% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.5b	(.f64 x (.f64 x -1/2))
	20.6b	x
✓	0.0b	(.f64 x (-.f64 1 (.f64 x 1/2)))
✓	0.0b	(+.f64 x (.f64 (.f64 x -1/2) x))

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes10.0ms (0.8%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 32 to 20 computations (37.5% saved)

regimes5.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 17 to 9 computations (47.1% saved)

regimes11.0ms (0.8%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

1 calls:

10.0ms

Results

Error	Segments	Branch
1.5b	3	`x`

Compiler

Compiled 10 to 5 computations (50% saved)

bsearch30.0ms (2.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	0.5645384811959887	4390.128249611582
14.0ms	-326855712.47714084	-3.4860170119536496e-6

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.3%)

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:

3.0ms

Results

Error	Segments	Branch
20.6b	1	`x`

Compiler

Compiled 5 to 2 computations (60% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	31	48
2	40	48
3	48	48
4	58	48
5	60	48
6	61	48

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 x (-.f64 1 (.f64 x 1/2)))
(+.f64 x (.f64 (.f64 x -1/2) x))
(if (<=.f64 x -5483728889062887/16777216) (.f64 x (.f64 x -1/2)) (if (<=.f64 x 5084910587101121/9007199254740992) x (.f64 x (.f64 x -1/2))))
x

Outputs
(.f64 x (-.f64 1 (.f64 x 1/2)))
(.f64 x (+.f64 1 (.f64 x -1/2)))
(+.f64 x (.f64 (.f64 x -1/2) x))
(+.f64 x (.f64 x (.f64 x -1/2)))
(if (<=.f64 x -5483728889062887/16777216) (.f64 x (.f64 x -1/2)) (if (<=.f64 x 5084910587101121/9007199254740992) x (.f64 x (.f64 x -1/2))))
x

Compiler

Compiled 38 to 25 computations (34.2% saved)

soundness0.0ms (0%)

end73.0ms (5.2%)

Compiler: Compiled 35 to 22 computations (37.1% saved)

Details

analyze3.0ms (0.2%)

sample766.0ms (55.1%)

preprocess28.0ms (2%)

simplify18.0ms (1.3%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

localize8.0ms (0.6%)

series2.0ms (0.1%)

rewrite47.0ms (3.4%)

simplify136.0ms (9.8%)

eval6.0ms (0.4%)

prune4.0ms (0.3%)

localize5.0ms (0.3%)

localize7.0ms (0.5%)

series1.0ms (0.1%)

rewrite50.0ms (3.6%)

simplify142.0ms (10.2%)

eval12.0ms (0.9%)

prune7.0ms (0.5%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes10.0ms (0.8%)

regimes5.0ms (0.4%)

regimes11.0ms (0.8%)

bsearch30.0ms (2.1%)

regimes4.0ms (0.3%)

simplify6.0ms (0.4%)

soundness0.0ms (0%)

end73.0ms (5.2%)

Profiling