Details

analyze4.0ms (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%	100%	0%	0%	0%	0%	2
33.3%	25%	50%	0%	0%	25%	0%	3
60%	37.5%	25%	0%	0%	37.5%	0%	4
77.8%	43.7%	12.5%	0%	0%	43.7%	0%	5
88.2%	46.9%	6.2%	0%	0%	46.9%	0%	6
93.9%	48.4%	3.1%	0%	0%	48.4%	0%	7
96.9%	49.2%	1.6%	0%	0%	49.2%	0%	8
98.4%	49.6%	0.8%	0%	0%	49.6%	0%	9
99.2%	49.8%	0.4%	0%	0%	49.8%	0%	10
99.6%	49.9%	0.2%	0%	0%	49.9%	0%	11
99.8%	49.9%	0.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.2s (72.9%)

Results

1.1s	4842×	body	256	valid
832.0ms	2075×	body	1024	valid
213.0ms	1090×	body	512	valid
68.0ms	249×	body	2048	valid
1.0ms	7×	body	256	invalid

Bogosity

preprocess8.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

2×	`rational.json-simplify-17`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	10	21
2	12	21
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))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`rational.json-simplify-17`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	10	21
2	12	21

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% 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

29.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0.1%)

Counts

1 → 1

Calls

3 calls:

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

rewrite107.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1318×	`rational.json-simplify-35`
1312×	`exponential.json-3`
1312×	`rational.json-1`
1312×	`rational.json-2`
1312×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	66	21
2	145	21
3	282	21
4	526	21
5	1164	21
6	2734	21
7	4450	21
8	6289	21

Stop Event

1×	node limit

Counts

1 → 52

Calls

Call 1

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

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

Outputs

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

simplify621.0ms (20.7%)

Algorithm

1×	egg-herbie

Rules

2802×	`rational.json-simplify-35`
1718×	`rational.json-simplify-1`
1436×	`rational.json-simplify-2`
890×	`rational.json-simplify-51`
764×	`rational.json-simplify-41`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1749
1	220	1749
2	824	1349
3	1797	1149
4	3313	1149
5	4517	1149
6	5292	1149
7	6122	1149
8	6504	1149
9	6684	1149
10	6849	1149
11	7299	1149
12	7482	1149
13	7652	1149
14	7659	1149
15	7670	1149
16	7672	1149
17	7675	1149
18	7829	1149
19	7983	1149

Stop Event

1×	node limit

Counts

53 → 58

Calls

Call 1

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

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

eval14.0ms (0.5%)

Compiler: Compiled 664 to 480 computations (27.7% saved)

prune7.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	2	59

Error

28.5b

Counts

59 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	31.0b	1

Compiler

Compiled 10 to 8 computations (20% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

28.5b

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	31.0b	1

Compiler

Compiled 10 to 8 computations (20% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

28.5b

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	31.0b	1

Compiler

Compiled 10 to 8 computations (20% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

28.5b

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	31.0b	1

Compiler

Compiled 10 to 8 computations (20% saved)

regimes7.0ms (0.2%)

Accuracy

Total -2.6b remaining (-8.8%)

Threshold costs -2.6b (-8.8%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Results

Error	Segments	Branch
29.3b	1	`x`
29.3b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 10 to 8 computations (20% saved)

soundness0.0ms (0%)

end17.0ms (0.6%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

Details

analyze4.0ms (0.1%)

sample2.2s (72.9%)

preprocess8.0ms (0.3%)

simplify9.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.3%)

series2.0ms (0.1%)

rewrite107.0ms (3.6%)

simplify621.0ms (20.7%)

eval14.0ms (0.5%)

prune7.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes7.0ms (0.2%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end17.0ms (0.6%)

Profiling