Details

analyze3.0ms (0.1%)

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)

sample712.0ms (18.8%)

Results

701.0ms	8256×	body	256	valid
1.0ms	13×	body	256	invalid

Bogosity

preprocess11.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

4×	`rational.json-simplify-2`
2×	`rational.json-simplify-16`
2×	`exponential.json-simplify-20`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	16	17
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))
(sqrt.f64 (*.f64 x (+.f64 x -1)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`rational.json-simplify-2`
2×	`rational.json-simplify-16`
2×	`exponential.json-simplify-20`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	16	17

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

eval0.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.2b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
▶	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.6b	(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
1.0ms	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)))

rewrite223.0ms (5.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1484×	`rational.json-simplify-35`
1344×	`exponential.json-3`
1344×	`rational.json-1`
1344×	`rational.json-2`
1344×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	56	17
2	120	17
3	228	17
4	419	17
5	912	17
6	2299	17
7	4049	17
8	5239	17
9	6733	17
10	7544	17
11	7544	17

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 0)))) (#(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 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2) (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)))) (#(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 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))))

simplify2.3s (60.3%)

Algorithm

1×	egg-herbie

Rules

6504×	`rational.json-simplify-51`
3738×	`rational.json-simplify-35`
1340×	`rational.json-simplify-49`
1200×	`rational.json-simplify-2`
900×	`rational.json-simplify-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	630
1	162	622
2	485	622
3	1265	622
4	2000	622
5	2731	622
6	3093	622
7	3179	622
8	3239	622
9	3279	622
10	3318	622
11	3357	622
12	3396	622
13	3435	622
14	3474	622
15	3513	622
16	3552	622
17	3591	622
18	3630	622
19	4534	622
20	4796	622
21	4896	622
22	4992	622
23	5086	622
24	5086	622
25	5299	622
26	5299	622
27	5392	622
28	5485	622
29	5578	622
30	5671	622
31	5764	622
32	5857	622
33	5950	622
34	6043	622
35	6136	622
36	6229	622

Stop Event

1×	node limit

Counts

34 → 47

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 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))
(+.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1)
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x -1))))
(.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2)
(.f64 4 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4) 1/4)
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8) 1/8)
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2) 2)
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4) 4)
(.f64 1/8 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))))) 256)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)

Outputs
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 x (+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(-.f64 x (+.f64 (+.f64 1/2 (.f64 1/8 (/.f64 1 x))) (.f64 1/16 (/.f64 1 (pow.f64 x 2)))))
(*.f64 -1 x)
(*.f64 x -1)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (*.f64 x -1))
(+.f64 1/2 (neg.f64 x))
(+.f64 1/2 (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (.f64 x -1)))
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (neg.f64 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 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/8 (/.f64 1 x)) (*.f64 x -1))))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (+.f64 (neg.f64 x) (.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (neg.f64 x))))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (neg.f64 x))))
(+.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(+.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 1 (sqrt.f64 (.f64 x (+.f64 x -1))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 4 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4) 1/4)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8) 1/8)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2) 2)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4) 4)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(.f64 1/8 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 4)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 8)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)) 16)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))) 32)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))) 64)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) 128)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))))) 256)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite196.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1834×	`rational.json-simplify-35`
1748×	`rational.json-simplify-1`
1416×	`exponential.json-3`
1416×	`rational.json-1`
1416×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	70	17
2	157	17
3	283	17
4	519	17
5	1128	17
6	2701	17
7	4667	17
8	5690	17
9	6936	17
10	7961	17
11	7961	17

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2) (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))))

simplify173.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1030×	`rational.json-simplify-35`
912×	`rational.json-simplify-2`
864×	`rational.json-simplify-1`
800×	`rational.json-simplify-46`
784×	`rational.json-simplify-19`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	467
1	177	435
2	289	435
3	903	435
4	1618	435
5	2262	435
6	2626	435
7	2741	435
8	2877	435
9	3134	435
10	3966	435
11	6039	435
12	7400	435

Stop Event

1×	node limit

Counts

23 → 36

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)))))
(+.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))
(+.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 8)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))))) 256)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))

Outputs
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 x (+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 -1 (.f64 x 1))
(neg.f64 x)
(+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 1/2 (.f64 -1 (.f64 x 1)))
(+.f64 1/2 (neg.f64 x))
(+.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 1/2 (.f64 -1 (.f64 x 1))) (*.f64 1/8 (/.f64 1 x)))
(+.f64 (+.f64 1/2 (neg.f64 x)) (*.f64 1/8 (/.f64 1 x)))
(+.f64 1/2 (+.f64 (neg.f64 x) (*.f64 1/8 (/.f64 1 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 (.f64 1/8 (/.f64 1 x)) (+.f64 (.f64 -1 (.f64 x 1)) (+.f64 1/2 (.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (.f64 1/8 (/.f64 1 x)) (+.f64 (neg.f64 x) (+.f64 1/2 (.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (+.f64 (+.f64 1/2 (neg.f64 x)) (.f64 1/8 (/.f64 1 x))) (.f64 1/16 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 x)) (+.f64 (neg.f64 x) (.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 1/2 (+.f64 (+.f64 (.f64 1/8 (/.f64 1 x)) (.f64 1/16 (/.f64 1 (pow.f64 x 2)))) (neg.f64 x)))
(+.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(+.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2) (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 1/2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(-.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 0)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 2) 2)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 4) 4)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8) 8)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)) 16)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))) 32)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))) 64)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (.f64 x (+.f64 x -1))) 8))))) 128)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 8)))))) 256)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (*.f64 x (+.f64 x -1)))

eval85.0ms (2.2%)

Compiler: Compiled 946 to 763 computations (19.3% saved)

prune8.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	81	4	85

Error

0.0b

Counts

85 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
▶	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.4b	x

Compiler

Compiled 23 to 17 computations (26.1% saved)

localize3.0ms (0.1%)

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

localize10.0ms (0.3%)

Compiler: Compiled 29 to 23 computations (20.7% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
✓	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.4b	x

Compiler

Compiled 23 to 17 computations (26.1% saved)

eval0.0ms (0%)

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

prune3.0ms (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

0.0b

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
✓	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.4b	x

Compiler

Compiled 23 to 17 computations (26.1% saved)

eval0.0ms (0%)

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

prune2.0ms (0%)

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

0.0b

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
✓	0.8b	(-.f64 x 1/2)
✓	30.8b	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	1.4b	x

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes10.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
4.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))`

Compiler

Compiled 37 to 26 computations (29.7% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.5b	1	`x`

Compiler

Compiled 22 to 15 computations (31.8% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.6b remaining (-81.6%)

Threshold costs -0.6b (-81.6%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(-.f64 x 1/2)

Outputs
(-.f64 x 1/2)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
0.8b	1	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 24 to 18 computations (25% saved)

soundness0.0ms (0%)

end23.0ms (0.6%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

Details

analyze3.0ms (0.1%)

sample712.0ms (18.8%)

preprocess11.0ms (0.3%)

simplify8.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite223.0ms (5.9%)

simplify2.3s (60.3%)

localize8.0ms (0.2%)

series1.0ms (0%)

rewrite196.0ms (5.2%)

simplify173.0ms (4.6%)

eval85.0ms (2.2%)

prune8.0ms (0.2%)

localize3.0ms (0.1%)

localize10.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes10.0ms (0.3%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end23.0ms (0.6%)

Profiling