Details

analyze71.0ms (3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
63.2%	56.2%	32.8%	0.1%	10.9%	0%	0%	8
74.3%	65.6%	22.6%	0.1%	11.7%	0%	0%	9
79.6%	65.6%	16.8%	0.1%	17.6%	0%	0%	10
85.9%	70.2%	11.5%	0.1%	18.1%	0%	0%	11
89.2%	70.2%	8.5%	0.1%	21.2%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

sample837.0ms (35.3%)

Results

785.0ms	8254×	body	256	valid
35.0ms	426×	body	256	infinite
0.0ms	2×	body	1024	valid

Bogosity

preprocess39.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

330×	`fma-def_binary64`
192×	`fma-neg_binary64`
60×	`cancel-sign-sub-inv_binary64`
56×	`distribute-rgt-in_binary64`
37×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	38	20
3	82	20
4	147	20
5	210	20
6	391	20
7	692	20
8	1085	20
9	1191	20
10	1209	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify25.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

230×	`fma-def_binary64`
111×	`fma-neg_binary64`
43×	`distribute-rgt-in_binary64`
39×	`cancel-sign-sub-inv_binary64`
28×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	22	10
3	48	10
4	84	10
5	118	10
6	209	10
7	357	10
8	552	10
9	722	10
10	822	10
11	838	10

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(.f64 1/2 (-.f64 (.f64 x x) y))

Compiler

Compiled 9 to 6 computations (33.3% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/2 (-.f64 (.f64 x x) y))

Compiler

Compiled 20 to 7 computations (65% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite57.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

773×	`pow1_binary64`
721×	`add-log-exp_binary64`
721×	`log1p-expm1-u_binary64`
721×	`expm1-log1p-u_binary64`
705×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	152	10
2	1974	10

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

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

Outputs

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

simplify190.0ms (8%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
558×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
450×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	231
1	19	231
2	32	231
3	57	231
4	123	231
5	350	231
6	1283	231
7	2184	231
8	2348	231
9	2532	231
10	2740	231
11	3038	231
12	3433	231
13	3912	231
14	4478	231
15	5170	231
16	6007	231
17	6397	231
18	6689	231
19	6969	231
20	7039	231
21	7075	231

Stop Event

1×	node limit

Counts

41 → 22

Calls

Call 1

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

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

eval9.0ms (0.4%)

Compiler: Compiled 227 to 123 computations (45.8% saved)

prune15.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Error

0.2b

Counts

23 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 1/2 (-.f64 (.f64 x x) y))
▶	19.7b	(*.f64 -1/2 y)
▶	43.0b	(.f64 1/2 (.f64 x x))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize7.0ms (0.3%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/2 (.f64 x x))

Compiler

Compiled 12 to 6 computations (50% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite64.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`pow1_binary64`
420×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
401×	`add-log-exp_binary64`
401×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1147	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 1/2) (.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/2 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/2 (.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/2 (.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/2 (*.f64 x x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))))))

simplify188.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
456×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	22	84
3	44	84
4	106	84
5	334	84
6	1259	84
7	2136	84
8	2300	84
9	2484	84
10	2692	84
11	2991	84
12	3384	84
13	3865	84
14	4433	84
15	5121	84
16	5954	84
17	6346	84
18	6636	84
19	6910	84
20	6982	84
21	7018	84
22	7959	84

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

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

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))

eval7.0ms (0.3%)

Compiler: Compiled 142 to 92 computations (35.2% saved)

prune8.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	15	4	19

Error

0.0b

Counts

19 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 1/2 (-.f64 (.f64 x x) y))
✓	19.7b	(*.f64 -1/2 y)
✓	43.0b	(.f64 1/2 (.f64 x x))
▶	43.0b	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)

Compiler

Compiled 29 to 22 computations (24.1% saved)

localize18.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
✓	0.4b	(*.f64 x (sqrt.f64 1/2))

Compiler

Compiled 17 to 14 computations (17.6% saved)

series7.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 x (sqrt.f64 1/2))
1.0ms	x	@	0	(*.f64 x (sqrt.f64 1/2))
1.0ms	x	@	-inf	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
1.0ms	x	@	0	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
1.0ms	x	@	inf	(*.f64 x (sqrt.f64 1/2))

rewrite91.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`pow1_binary64`
513×	`add-log-exp_binary64`
513×	`log1p-expm1-u_binary64`
513×	`expm1-log1p-u_binary64`
500×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	146	13
2	1518	13

Stop Event

1×	node limit

Counts

2 → 35

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)

Outputs

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

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

simplify211.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

834×	`sqr-pow_binary64`
692×	`cube-prod_binary64`
684×	`fabs-mul_binary64`
648×	`associate-l_binary64`
573×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	216
1	19	156
2	37	156
3	95	156
4	391	156
5	2142	156
6	2255	156
7	2468	156
8	2664	156
9	2897	156
10	3202	156
11	3826	156
12	4301	156
13	4925	156
14	5637	156
15	6558	156
16	7080	156
17	7468	156
18	7834	156
19	7934	156
20	7964	156

Stop Event

1×	node limit

Counts

59 → 38

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))

Outputs
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 x x))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))

eval19.0ms (0.8%)

Compiler: Compiled 347 to 262 computations (24.5% saved)

prune41.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	39	3	42

Error

Counts

42 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 1/2 (-.f64 (.f64 x x) y))
✓	19.7b	(*.f64 -1/2 y)
▶	42.8b	(.f64 x (.f64 x 1/2))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize11.0ms (0.5%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune4.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 1/2 (-.f64 (.f64 x x) y))
✓	19.7b	(*.f64 -1/2 y)
✓	42.8b	(.f64 x (.f64 x 1/2))

Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes72.0ms (3%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

31.0ms	y
11.0ms	(-.f64 (*.f64 x x) y)
10.0ms	(.f64 1/2 (-.f64 (.f64 x x) y))
10.0ms	x
7.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.2b	1	`x`
0.2b	1	`y`
0.2b	1	`(.f64 1/2 (-.f64 (.f64 x x) y))`
0.2b	1	`(-.f64 (*.f64 x x) y)`
0.2b	1	`(*.f64 x x)`

Compiler

Compiled 55 to 35 computations (36.4% saved)

regimes226.0ms (9.5%)

Accuracy

Total -51.9b remaining (-532.2%)

Threshold costs -51.9b (-532.2%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

4 calls:

130.0ms	x
71.0ms	y
12.0ms	(*.f64 x x)
10.0ms	(*.f64 x x)

Results

Error	Segments	Branch
9.7b	3	`x`
12.3b	7	`y`
10.0b	2	`(*.f64 x x)`
10.0b	2	`(*.f64 x x)`

Compiler

Compiled 31 to 20 computations (35.5% saved)

bsearch63.0ms (2.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
32.0ms	2.969774585051767e-30	4.179480300937361e-17
31.0ms	-431912211370920500.0	-4914532721904700.0

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	44
1	24	44
2	29	44
3	31	44
4	32	44

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(*.f64 1/2 (-.f64 (*.f64 x x) y))

(if (<=.f64 x -431912211370920512) (*.f64 x (*.f64 x 1/2)) (if (<=.f64 x 2119301962185967/713623846352979940529142984724747568191373312) (*.f64 -1/2 y) (*.f64 x (*.f64 x 1/2))))

(*.f64 -1/2 y)

Outputs
(.f64 1/2 (-.f64 (.f64 x x) y))
(if (<=.f64 x -431912211370920512) (.f64 x (.f64 x 1/2)) (if (<=.f64 x 2119301962185967/713623846352979940529142984724747568191373312) (.f64 -1/2 y) (.f64 x (*.f64 x 1/2))))
(if (<=.f64 x -431912211370920512) (.f64 x (.f64 1/2 x)) (if (<=.f64 x 2119301962185967/713623846352979940529142984724747568191373312) (.f64 y -1/2) (.f64 x (*.f64 1/2 x))))
(*.f64 -1/2 y)
(*.f64 y -1/2)

Compiler

Compiled 37 to 26 computations (29.7% saved)

soundness0.0ms (0%)

end56.0ms (2.4%)

Compiler: Compiled 33 to 22 computations (33.3% saved)

Iter	Nodes	Cost
0	7	10
1	11	10
2	22	10
3	48	10
4	84	10
5	118	10
6	209	10
7	357	10
8	552	10
9	722	10
10	822	10
11	838	10

Iter	Nodes	Cost
0	7	10
1	11	10
2	22	10
3	48	10
4	84	10
5	118	10
6	209	10
7	357	10
8	552	10
9	722	10
10	822	10
11	838	10

Details

analyze71.0ms (3%)

sample837.0ms (35.3%)

preprocess39.0ms (1.6%)

simplify25.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.3%)

series3.0ms (0.1%)

rewrite57.0ms (2.4%)

simplify190.0ms (8%)

eval9.0ms (0.4%)

prune15.0ms (0.6%)

localize7.0ms (0.3%)

localize10.0ms (0.4%)

series3.0ms (0.1%)

rewrite64.0ms (2.7%)

simplify188.0ms (7.9%)

eval7.0ms (0.3%)

prune8.0ms (0.3%)

localize18.0ms (0.8%)

series7.0ms (0.3%)

rewrite91.0ms (3.9%)

simplify211.0ms (8.9%)

eval19.0ms (0.8%)

prune41.0ms (1.7%)

localize11.0ms (0.5%)

eval0.0ms (0%)

prune4.0ms (0.2%)

regimes72.0ms (3%)

regimes226.0ms (9.5%)

bsearch63.0ms (2.7%)

simplify10.0ms (0.4%)

soundness0.0ms (0%)

end56.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	7	10
1	11	10
2	22	10
3	48	10
4	84	10
5	118	10
6	209	10
7	357	10
8	552	10
9	722	10
10	822	10
11	838	10