Details

analyze5.0ms (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
0%	0%	100%	0%	0%	0%	0%	3
62.5%	62.5%	37.5%	0%	0%	0%	0%	4
81.3%	81.2%	18.7%	0%	0%	0%	0%	5
90.6%	90.6%	9.4%	0%	0%	0%	0%	6
95.3%	95.3%	4.7%	0%	0%	0%	0%	7
97.7%	97.6%	2.3%	0%	0%	0%	0%	8
98.8%	98.8%	1.2%	0%	0%	0%	0%	9
99.4%	99.4%	0.6%	0%	0%	0%	0%	10
99.7%	99.7%	0.3%	0%	0%	0%	0%	11
99.9%	99.8%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample3.1s (87.1%)

Results

1.9s	4145×	body	2048	valid
1.2s	4111×	body	256	valid

Bogosity

preprocess83.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

1836×	`rational.json-simplify-35`
1348×	`rational.json-simplify-53`
1006×	`rational.json-simplify-39`
870×	`rational.json-simplify-59`
690×	`rational.json-simplify-41`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	18	35
2	27	35
3	52	35
4	209	35
5	1996	35
6	6050	35
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify86.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1836×	`rational.json-simplify-35`
1348×	`rational.json-simplify-53`
1006×	`rational.json-simplify-39`
870×	`rational.json-simplify-59`
690×	`rational.json-simplify-41`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	18	35
2	27	35
3	52	35
4	209	35
5	1996	35
6	6050	35

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% 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

31.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.3b	(-.f64 (/.f64 x x) (.f64 (/.f64 1 x) (sqrt.f64 (.f64 x x))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 x) (sqrt.f64 (.f64 x x)))
✓	4.8b	(-.f64 (/.f64 x x) (.f64 (/.f64 1 x) (sqrt.f64 (.f64 x x))))
✓	28.3b	(sqrt.f64 (*.f64 x x))

Compiler

Compiled 36 to 14 computations (61.1% saved)

series1.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite84.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1600×	`rational.json-1`
1600×	`rational.json-2`
1600×	`rational.json-4`
1600×	`rational.json-3`
1592×	`exponential.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	69
1	83	57
2	193	51
3	485	51
4	1581	51
5	4936	51

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

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

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

Outputs

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

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

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

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1200×	`rational.json-simplify-2`
938×	`rational.json-simplify-46`
906×	`rational.json-simplify-61`
880×	`rational.json-simplify-35`
868×	`rational.json-simplify-43`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	161	1641
1	414	1545
2	1264	1545
3	4307	1545

Stop Event

1×	node limit

Counts

121 → 94

Calls

Call 1

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

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

eval15.0ms (0.4%)

Compiler: Compiled 1321 to 546 computations (58.7% saved)

prune12.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	2	95

Error

Counts

95 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	30.8b	2
	31.2b	0

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	30.8b	2
	31.2b	0

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	30.8b	2
	31.2b	0

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	30.8b	2
	31.2b	0

Compiler

Compiled 4 to 4 computations (0% saved)

regimes11.0ms (0.3%)

Accuracy

Total -62.5b remaining (-∞%)

Threshold costs -62.5b (-∞%)

Counts

3 → 2

Calls

Call 1

Inputs
0
2
(-.f64 (/.f64 x x) (.f64 (/.f64 1 x) (sqrt.f64 (.f64 x x))))

Outputs
2
0

Calls

2 calls:

6.0ms	x
4.0ms	(-.f64 (/.f64 x x) (.f64 (/.f64 1 x) (sqrt.f64 (.f64 x x))))

Results

Error	Segments	Branch
0b	2	`x`
5.3b	2	`(-.f64 (/.f64 x x) (.f64 (/.f64 1 x) (sqrt.f64 (.f64 x x))))`

Compiler

Compiled 30 to 19 computations (36.7% saved)

bsearch30.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
30.0ms	-8.909109564615278e-306	3.9898614134953596e-307

Results

22.0ms	64×	body	2048	valid
7.0ms	64×	body	256	valid

Compiler

Compiled 65 to 59 computations (9.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) 2 0)

Outputs

(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) 2 0)

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness0.0ms (0%)

end18.0ms (0.5%)

Compiler: Compiled 8 to 7 computations (12.5% saved)

Details

analyze5.0ms (0.1%)

sample3.1s (87.1%)

preprocess83.0ms (2.3%)

simplify86.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize12.0ms (0.3%)

series1.0ms (0%)

rewrite84.0ms (2.3%)

simplify100.0ms (2.8%)

eval15.0ms (0.4%)

prune12.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes11.0ms (0.3%)

bsearch30.0ms (0.8%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end18.0ms (0.5%)

Profiling