Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample643.0ms (33.8%)

Results

632.0ms	8256×	body	256	valid
1.0ms	6×	body	256	invalid

Bogosity

preprocess137.0ms (7.2%)

Algorithm

2×	egg-herbie

Rules

1810×	`rational.json-simplify-35`
1350×	`rational.json-simplify-53`
1056×	`rational.json-simplify-19`
1026×	`rational.json-simplify-39`
864×	`rational.json-simplify-59`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	9	17
2	13	17
3	31	17
4	180	17
5	1937	17
6	5866	17
7	7749	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify138.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

1810×	`rational.json-simplify-35`
1350×	`rational.json-simplify-53`
1056×	`rational.json-simplify-19`
1026×	`rational.json-simplify-39`
864×	`rational.json-simplify-59`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	9	17
2	13	17
3	31	17
4	180	17
5	1937	17
6	5866	17
7	7749	17

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite61.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1418×	`rational.json-simplify-2`
1310×	`rational.json-1`
1310×	`rational.json-2`
1310×	`rational.json-4`
1310×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	60	17
2	139	17
3	313	17
4	1137	17
5	4361	17

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

Outputs

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

simplify108.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1104×	`rational.json-simplify-2`
1058×	`rational.json-simplify-59`
882×	`rational.json-simplify-1`
698×	`rational.json-simplify-51`
662×	`rational.json-simplify-44`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	79	851
1	170	843
2	329	843
3	730	843
4	1830	771
5	4677	771
6	6836	771

Stop Event

1×	node limit

Counts

27 → 58

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(+.f64 0 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)
(.f64 2 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2))
(.f64 (.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2)
(.f64 1/2 (.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2))
(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2) 2)
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(/.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 4)) 8)
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 4)) (.f64 2 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 4))) 16)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (*.f64 -1/16 (pow.f64 x 6)))))
(+.f64 1 (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))) (*.f64 -1/16 (pow.f64 x 6))))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(+.f64 (.f64 x (sqrt.f64 -1)) (.f64 1/2 (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (.f64 x (sqrt.f64 -1)) (.f64 1/2 (/.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 x (sqrt.f64 -1)) (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1))))) (.f64 1/8 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (-.f64 (.f64 x (sqrt.f64 -1)) (.f64 1/8 (/.f64 (/.f64 1 (sqrt.f64 -1)) (pow.f64 x 3)))))
(+.f64 (.f64 x (sqrt.f64 -1)) (-.f64 (.f64 1/2 (/.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (+.f64 (.f64 x (sqrt.f64 -1)) (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1))))) (.f64 1/16 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 5))))) (.f64 1/8 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (+.f64 (.f64 x (sqrt.f64 -1)) (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1))))) (-.f64 (.f64 1/16 (/.f64 (/.f64 1 (pow.f64 x 5)) (sqrt.f64 -1))) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3))))))
(+.f64 (.f64 x (sqrt.f64 -1)) (+.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3))))) (.f64 1/16 (/.f64 (/.f64 1 (pow.f64 x 5)) (sqrt.f64 -1)))))
(+.f64 (.f64 x (sqrt.f64 -1)) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 5)))) (-.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 1/8 (/.f64 (/.f64 1 (sqrt.f64 -1)) (pow.f64 x 3))))))
(+.f64 (.f64 x (sqrt.f64 -1)) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 -1) x)) (-.f64 (.f64 1/16 (/.f64 (sqrt.f64 -1) (pow.f64 x 5))) (.f64 1/8 (/.f64 (sqrt.f64 -1) (pow.f64 x 3))))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(.f64 -1 (.f64 x (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (.f64 -1 (.f64 x (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))))
(-.f64 (.f64 (sqrt.f64 -1) (neg.f64 x)) (.f64 1/2 (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (.f64 x (neg.f64 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (.f64 (sqrt.f64 -1) (neg.f64 x)) (.f64 1/2 (/.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (.f64 -1 (.f64 x (sqrt.f64 -1)))) (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))))
(+.f64 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (-.f64 (.f64 (sqrt.f64 -1) (neg.f64 x)) (.f64 1/2 (/.f64 1 (*.f64 x (sqrt.f64 -1))))))
(+.f64 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (-.f64 (.f64 x (neg.f64 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 x (sqrt.f64 -1))))))
(+.f64 (.f64 x (neg.f64 (sqrt.f64 -1))) (-.f64 (.f64 1/8 (/.f64 (/.f64 1 (sqrt.f64 -1)) (pow.f64 x 3))) (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1))))))
(+.f64 (.f64 (sqrt.f64 -1) (neg.f64 x)) (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 -1) (pow.f64 x 3))) (*.f64 1/2 (/.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (.f64 -1 (.f64 x (sqrt.f64 -1)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 1/16 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 5))))))
(+.f64 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (-.f64 (.f64 (sqrt.f64 -1) (neg.f64 x)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 1/16 (/.f64 (/.f64 1 (pow.f64 x 5)) (sqrt.f64 -1))))))
(+.f64 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (-.f64 (.f64 x (neg.f64 (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 1/16 (/.f64 (/.f64 1 (pow.f64 x 5)) (sqrt.f64 -1))))))
(+.f64 (.f64 x (neg.f64 (sqrt.f64 -1))) (-.f64 (.f64 1/8 (/.f64 (/.f64 1 (sqrt.f64 -1)) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 x (sqrt.f64 -1)))) (.f64 1/16 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 5)))))))
(+.f64 (.f64 (sqrt.f64 -1) (neg.f64 x)) (-.f64 (.f64 1/8 (/.f64 (sqrt.f64 -1) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 -1) x)) (.f64 1/16 (/.f64 (sqrt.f64 -1) (pow.f64 x 5))))))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.f64 0 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 2 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 1/2 (.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2) 2)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2) 2)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(/.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 4) 4)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 4)) 8)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 4)) (.f64 2 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 4))) 16)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(sqrt.f64 (-.f64 1 (*.f64 x x)))

eval20.0ms (1.1%)

Compiler: Compiled 1041 to 873 computations (16.1% saved)

prune7.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	3	59

Error

Counts

59 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.6b	1

Compiler

Compiled 17 to 14 computations (17.6% saved)

localize8.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite255.0ms (13.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1992×	`rational.json-simplify-2`
1632×	`rational.json-simplify-35`
1580×	`rational.json-simplify-1`
1152×	`exponential.json-3`
1152×	`rational.json-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	45	13
2	95	13
3	179	13
4	318	13
5	682	13
6	1650	13
7	2848	13
8	3555	13
9	4343	13
10	5393	13
11	6046	13
12	6203	13
13	6453	13
14	7311	13
15	7560	13

Stop Event

1×	node limit

Counts

1 → 47

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -1/2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 -1/2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (+.f64 -1 (+.f64 1 (.f64 (pow.f64 x 2) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x 2) -1/4) (.f64 (pow.f64 x 2) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 -1 (.f64 (pow.f64 x 2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (.f64 (pow.f64 x 2) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (+.f64 -1 (.f64 (pow.f64 x 2) 1/2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (+.f64 -1 (+.f64 1 (.f64 (pow.f64 x 2) 1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 -1/2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 -1 (+.f64 1 (.f64 (pow.f64 x 2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (+.f64 1 (.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (+.f64 -1 (.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 1 (.f64 (pow.f64 x 2) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1/2 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 x 2)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 x 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) 4) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) -2) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) -4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) 8) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 x 2) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (pow.f64 x 2) 8)) -32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (pow.f64 x 2) -4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8))) -64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (pow.f64 x 2) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8)))) -128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8))))) -256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8)))))) -512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (+.f64 1 (.f64 (pow.f64 x 2) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/2 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 -1 (+.f64 1 (.f64 (pow.f64 x 2) 1/2))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/2 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 2) -1/4) (*.f64 (pow.f64 x 2) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 2)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 x 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 4) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) -2) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) -4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 8) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 2) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 x 2) 8)) -32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 x 2) -4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) -4))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 8))) -64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 x 2) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (pow.f64 x 2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 (pow.f64 x 2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 (pow.f64 x 2) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 8)))) -128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) -4)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) -4))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 (pow.f64 x 2) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 (pow.f64 x 2) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 8))))) -256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) -4)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) 8)))))) -512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 (pow.f64 x 2) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 (pow.f64 x 2) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 x 2) -4))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (pow.f64 x 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))))))))

simplify217.0ms (11.4%)

Algorithm

1×	egg-herbie

Rules

2928×	`rational.json-simplify-45`
1802×	`rational.json-simplify-2`
1792×	`rational.json-simplify-35`
956×	`rational.json-simplify-1`
724×	`rational.json-simplify-49`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	611
1	290	611
2	533	611
3	1300	611
4	2911	611
5	3687	611
6	4231	611
7	5259	611
8	5552	611
9	5849	611
10	5971	611
11	6120	611
12	6245	611

Stop Event

1×	node limit

Counts

47 → 48

Calls

Call 1

Inputs
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 -1 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)))
(+.f64 -1 (-.f64 1 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))))
(+.f64 (.f64 (pow.f64 x 2) -1/4) (.f64 (pow.f64 x 2) -1/4))
(+.f64 -2 (-.f64 1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2))))
(+.f64 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)) -1)
(+.f64 (-.f64 1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2))) -2)
(+.f64 (-.f64 1 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))) -1)
(-.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(-.f64 0 (*.f64 (pow.f64 x 2) 1/2))
(-.f64 0 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))))
(-.f64 1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))
(-.f64 -1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2)))
(-.f64 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)) 1)
(/.f64 (pow.f64 x 2) -2)
(/.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(/.f64 (*.f64 2 (pow.f64 x 2)) -4)
(/.f64 (neg.f64 (pow.f64 x 2)) 2)
(/.f64 (*.f64 (pow.f64 x 2) 4) -8)
(/.f64 (*.f64 (pow.f64 x 2) -2) 4)
(/.f64 (*.f64 (pow.f64 x 2) -4) 8)
(/.f64 (*.f64 (pow.f64 x 2) 8) -16)
(/.f64 (*.f64 (pow.f64 x 2) 1/2) -1)
(/.f64 (.f64 2 (.f64 (pow.f64 x 2) 8)) -32)
(/.f64 (.f64 2 (.f64 (pow.f64 x 2) -4)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) -4))) 32)
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 8))) -64)
(/.f64 (neg.f64 (*.f64 (pow.f64 x 2) 8)) 16)
(/.f64 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8))) 32)
(/.f64 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8))) 32)
(/.f64 (.f64 2 (neg.f64 (.f64 2 (*.f64 (pow.f64 x 2) 8)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8)))) -128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) -4))))) 128)
(/.f64 (.f64 2 (.f64 2 (neg.f64 (*.f64 (pow.f64 x 2) 8)))) 64)
(/.f64 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 8))))) -256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4)))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8)))))) -512)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (*.f64 (pow.f64 x 2) 8)))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) -4))))))) 512)
(/.f64 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))) -1)
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(neg.f64 (*.f64 (pow.f64 x 2) 1/2))
(neg.f64 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))))

Outputs
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 -1 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 -1 (-.f64 1 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (.f64 (pow.f64 x 2) -1/4) (.f64 (pow.f64 x 2) -1/4))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 -2 (-.f64 1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2))))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)) -1)
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (-.f64 1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2))) -2)
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (-.f64 1 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))) -1)
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 (*.f64 -1/2 (pow.f64 x 2)) 0)
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 0 (*.f64 (pow.f64 x 2) 1/2))
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 0 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))))
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2)))
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 -1 (+.f64 -1 (*.f64 (pow.f64 x 2) 1/2)))
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 (-.f64 1 (*.f64 (pow.f64 x 2) 1/2)) 1)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (pow.f64 x 2) -2)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 2 (pow.f64 x 2)) -4)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (neg.f64 (pow.f64 x 2)) 2)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) 4) -8)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) -2) 4)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) -4) 8)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) 8) -16)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (*.f64 (pow.f64 x 2) 1/2) -1)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 (pow.f64 x 2) 8)) -32)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 (pow.f64 x 2) -4)) 16)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) -4))) 32)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 8))) -64)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (neg.f64 (*.f64 (pow.f64 x 2) 8)) 16)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8))) 32)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8))) 32)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (neg.f64 (.f64 2 (*.f64 (pow.f64 x 2) 8)))) 64)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8)))) -128)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4)))) 64)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) -4))))) 128)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (neg.f64 (*.f64 (pow.f64 x 2) 8)))) 64)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (.f64 (pow.f64 x 2) 8))))) 128)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) 8))))) -256)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) -4)))))) 256)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 x 2) 8)))))) -512)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 (pow.f64 x 2) 8))))) 128)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (neg.f64 (.f64 2 (*.f64 (pow.f64 x 2) 8)))))) 256)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (pow.f64 x 2) -4))))))) 512)
(*.f64 -1/2 (pow.f64 x 2))
(/.f64 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))) -1)
(*.f64 -1/2 (pow.f64 x 2))
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(*.f64 -1/2 (pow.f64 x 2))
(neg.f64 (*.f64 (pow.f64 x 2) 1/2))
(*.f64 -1/2 (pow.f64 x 2))
(neg.f64 (+.f64 -1 (+.f64 1 (*.f64 (pow.f64 x 2) 1/2))))
(*.f64 -1/2 (pow.f64 x 2))

eval15.0ms (0.8%)

Compiler: Compiled 584 to 535 computations (8.4% saved)

prune6.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.6b	1

Compiler

Compiled 17 to 14 computations (17.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.6b	1

Compiler

Compiled 17 to 14 computations (17.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.6b	1

Compiler

Compiled 17 to 14 computations (17.6% saved)

regimes130.0ms (6.8%)

Accuracy

Total -0.6b remaining (-14651%)

Threshold costs -0.6b (-14651%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

122.0ms	(*.f64 x x)
3.0ms	x
2.0ms	(-.f64 1 (*.f64 x x))
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(sqrt.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness0.0ms (0%)

end143.0ms (7.5%)

Compiler: Compiled 8 to 6 computations (25% saved)

Details

analyze3.0ms (0.2%)

sample643.0ms (33.8%)

preprocess137.0ms (7.2%)

simplify138.0ms (7.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.3%)

series1.0ms (0.1%)

rewrite61.0ms (3.2%)

simplify108.0ms (5.7%)

eval20.0ms (1.1%)

prune7.0ms (0.4%)

localize8.0ms (0.4%)

series1.0ms (0%)

rewrite255.0ms (13.4%)

simplify217.0ms (11.4%)

eval15.0ms (0.8%)

prune6.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes130.0ms (6.8%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end143.0ms (7.5%)

Profiling