Details

analyze587.0ms (2.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	74.9%	0.2%	0%	25%	0%	6
0%	0%	56.1%	0.2%	0%	43.7%	0%	7
0%	0%	42.1%	0.2%	0%	57.7%	0%	8
1.2%	0.4%	31.2%	0.2%	0%	68.2%	0%	9
2.2%	0.6%	25.7%	0.2%	0%	73.5%	0%	10
4%	0.9%	21.1%	0.2%	0%	77.9%	0%	11
7.2%	1.3%	17%	0.2%	0%	81.5%	0%	12

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample8.3s (31%)

Results

4.0s	15750×	body	256	invalid
2.2s	4473×	body	512	valid
1.4s	1783×	body	1024	valid
641.0ms	2000×	body	256	valid

Bogosity

preprocess82.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

799×	`sub-neg_binary64`
524×	`fma-neg_binary64`
468×	`distribute-rgt-in_binary64`
401×	`associate-+l+_binary64`
382×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	350
1	141	350
2	537	350
3	2852	350
4	4688	350
5	7021	350
0	4	4
1	4	4

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3

Outputs
0
1
0
2
0
3
0

Call 2

Inputs
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))

Outputs
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z))))) (sqrt.f64 z))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 t)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))

Symmetry

(sort x y z t)

Compiler

Compiled 39 to 31 computations (20.5% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
615×	`distribute-neg-in_binary64`
542×	`associate-+r-_binary64`
537×	`cancel-sign-sub-inv_binary64`
504×	`associate-+l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	54	50
2	168	50
3	974	50
4	4916	50

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Outputs
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 z)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))

eval1.0ms (0%)

Compiler: Compiled 66 to 46 computations (30.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

5.6b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	42.9b	(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))

Status

Error

Program

▶

5.7b

(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

▶

42.9b

(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))

Compiler

Compiled 70 to 54 computations (22.9% saved)

localize62.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t)))
✓	2.2b	(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))
✓	15.4b	(-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t)))))
✓	17.5b	(+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))

Compiler

Compiled 137 to 83 computations (39.4% saved)

series28.0ms (0.1%)

Counts

4 → 21

Calls

33 calls:

Time	Variable		Point	Expression
2.0ms	z	@	-inf	(+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))
1.0ms	t	@	inf	(+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))
1.0ms	t	@	-inf	(+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))
1.0ms	t	@	-inf	(-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t)))))
1.0ms	y	@	inf	(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))

rewrite111.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

321×	`add-sqr-sqrt_binary64`
318×	`*-un-lft-identity_binary64`
318×	`pow1_binary64`
297×	`add-cbrt-cube_binary64`
297×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	106
1	603	106

Stop Event

1×	node limit

Counts

4 → 151

Calls

Call 1

Inputs
(+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))
(-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t)))

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

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

689×	`sub-neg_binary64`
657×	`fma-def_binary64`
639×	`fma-neg_binary64`
559×	`associate-l_binary64`
455×	`associate--l+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	493
1	258	491
2	779	488
3	3013	481
4	4855	480
5	7234	480

Stop Event

1×	node limit

Counts

172 → 190

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 z) 1)
(sqrt.f64 z)
(-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t))))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(*.f64 -1 (sqrt.f64 (+.f64 1 t)))
(-.f64 (sqrt.f64 z) 1)
(-.f64 (+.f64 (sqrt.f64 z) (*.f64 -1/2 t)) 1)
(-.f64 (+.f64 (sqrt.f64 z) (+.f64 (.f64 1/8 (pow.f64 t 2)) (.f64 -1/2 t))) 1)
(-.f64 (+.f64 (sqrt.f64 z) (+.f64 (.f64 1/8 (pow.f64 t 2)) (+.f64 (.f64 -1/16 (pow.f64 t 3)) (*.f64 -1/2 t)))) 1)

Outputs
(-.f64 (sqrt.f64 z) 1)
(+.f64 (sqrt.f64 z) -1)
(sqrt.f64 z)
(-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))
(-.f64 (sqrt.f64 t) (hypot.f64 1 (sqrt.f64 t)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) (sqrt.f64 y))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))
(-.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))
(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t))))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 1 (-.f64 (+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 z 1))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))))
(+.f64 (+.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 t))) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 z 1))) (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (sqrt.f64 t))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))))
(+.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 z)) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
(+.f64 1 (+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 z 1))) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
(+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 t)) (sqrt.f64 (+.f64 z 1))) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 t) (+.f64 (sqrt.f64 z) (sqrt.f64 x))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 z 1))) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))
(+.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 t) (+.f64 (sqrt.f64 z) (sqrt.f64 x))))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))
(+.f64 1 (-.f64 (+.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 t))) (+.f64 (+.f64 (sqrt.f64 t) (sqrt.f64 y)) (sqrt.f64 x))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 t) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (+.f64 (sqrt.f64 t) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 x)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))
(-.f64 (+.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 t))) (+.f64 (+.f64 (sqrt.f64 t) (sqrt.f64 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (hypot.f64 1 (sqrt.f64 t)) (+.f64 (sqrt.f64 t) (+.f64 (sqrt.f64 y) (sqrt.f64 x))))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 t) (sqrt.f64 y)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (+.f64 (sqrt.f64 t) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 x))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 x))))
(+.f64 1 (+.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 x))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 x))))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
(*.f64 -1 (sqrt.f64 (+.f64 1 t)))
(neg.f64 (sqrt.f64 (+.f64 1 t)))
(neg.f64 (hypot.f64 1 (sqrt.f64 t)))
(-.f64 (sqrt.f64 z) 1)
(+.f64 (sqrt.f64 z) -1)
(-.f64 (+.f64 (sqrt.f64 z) (*.f64 -1/2 t)) 1)
(+.f64 (sqrt.f64 z) (-.f64 (*.f64 t -1/2) 1))
(+.f64 -1 (fma.f64 t -1/2 (sqrt.f64 z)))
(+.f64 (sqrt.f64 z) (fma.f64 t -1/2 -1))
(-.f64 (+.f64 (sqrt.f64 z) (+.f64 (.f64 1/8 (pow.f64 t 2)) (.f64 -1/2 t))) 1)
(+.f64 (sqrt.f64 z) (-.f64 (fma.f64 1/8 (.f64 t t) (.f64 t -1/2)) 1))
(+.f64 (sqrt.f64 z) (+.f64 (.f64 t (.f64 t 1/8)) (fma.f64 t -1/2 -1)))
(+.f64 (sqrt.f64 z) (fma.f64 t (*.f64 t 1/8) (fma.f64 t -1/2 -1)))
(fma.f64 t (fma.f64 t 1/8 -1/2) (+.f64 (sqrt.f64 z) -1))
(-.f64 (+.f64 (sqrt.f64 z) (+.f64 (.f64 1/8 (pow.f64 t 2)) (+.f64 (.f64 -1/16 (pow.f64 t 3)) (*.f64 -1/2 t)))) 1)
(+.f64 (sqrt.f64 z) (-.f64 (fma.f64 1/8 (.f64 t t) (fma.f64 -1/16 (pow.f64 t 3) (.f64 t -1/2))) 1))
(+.f64 (sqrt.f64 z) (+.f64 (fma.f64 1/8 (.f64 t t) (fma.f64 t -1/2 (.f64 -1/16 (pow.f64 t 3)))) -1))
(+.f64 (+.f64 (sqrt.f64 z) -1) (fma.f64 t -1/2 (.f64 (.f64 t t) (+.f64 1/8 (*.f64 t -1/16)))))
(+.f64 -1 (fma.f64 t (fma.f64 t 1/8 -1/2) (fma.f64 -1/16 (pow.f64 t 3) (sqrt.f64 z))))
(+.f64 (sqrt.f64 z) (fma.f64 t (+.f64 (*.f64 t (fma.f64 t -1/16 1/8)) -1/2) -1))

localize62.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	3.0b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 142 to 87 computations (38.7% saved)

series9.0ms (0%)

Counts

4 → 4

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	z	@	inf	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
1.0ms	t	@	inf	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
1.0ms	x	@	inf	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.0ms	y	@	inf	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
1.0ms	t	@	-inf	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite107.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

422×	`log1p-udef_binary64`
264×	`add-sqr-sqrt_binary64`
261×	`*-un-lft-identity_binary64`
261×	`pow1_binary64`
243×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	504	44
2	7388	44

Stop Event

1×	node limit

Counts

4 → 148

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

Outputs
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simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	4
1	4	4

Stop Event

1×

saturated

Counts

152 → 149

Calls

Call 1

Inputs
1
1
1
1

Outputs
1
1
1
1

eval638.0ms (2.4%)

Compiler: Compiled 14847 to 9400 computations (36.7% saved)

prune98.0ms (0.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	321	18	339
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	322	19	341

Error

0.8b

Counts

341 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	5.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
	43.0b	(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (-.f64 (sqrt.f64 t) (hypot.f64 1 (sqrt.f64 t)))))
▶	1.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	25.4b	(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (sqrt.f64 z)))
	6.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 (+.f64 1 y) y) (sqrt.f64 (*.f64 (+.f64 1 y) y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	5.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	19.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 y) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.3b	(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) 3))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
✓	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	42.5b	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
	42.5b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	39.5b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))

Compiler

Compiled 1309 to 1007 computations (23.1% saved)

localize102.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 y 1))
	0.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.0b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 181 to 106 computations (41.4% saved)

series3.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(sqrt.f64 (+.f64 y 1))
1.0ms	y	@	-inf	(sqrt.f64 (+.f64 y 1))
0.0ms	y	@	0	(sqrt.f64 (+.f64 y 1))

rewrite84.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

474×	`pow1_binary64`
462×	`add-sqr-sqrt_binary64`
453×	`*-un-lft-identity_binary64`
444×	`log1p-expm1-u_binary64`
444×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	103	6
2	1258	6

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 y 1))

Outputs

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

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-rgt-in_binary64`
606×	`distribute-lft-in_binary64`
536×	`unswap-sqr_binary64`
498×	`associate-l_binary64`
456×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	48	41
2	108	38
3	291	31
4	783	28
5	2360	28
6	4000	28
7	4228	28
8	4528	28
9	5067	28
10	6064	28

Stop Event

1×	node limit

Counts

27 → 30

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 y))
(+.f64 1 (+.f64 (.f64 1/2 y) (.f64 -1/8 (pow.f64 y 2))))
(+.f64 1 (+.f64 (.f64 1/2 y) (+.f64 (.f64 1/16 (pow.f64 y 3)) (*.f64 -1/8 (pow.f64 y 2)))))

Outputs
1
(+.f64 1 (*.f64 1/2 y))
(fma.f64 1/2 y 1)
(+.f64 1 (+.f64 (.f64 1/2 y) (.f64 -1/8 (pow.f64 y 2))))
(+.f64 1 (fma.f64 1/2 y (.f64 -1/8 (.f64 y y))))
(+.f64 1 (fma.f64 1/2 y (.f64 y (.f64 y -1/8))))
(fma.f64 y (*.f64 y -1/8) (fma.f64 1/2 y 1))
(fma.f64 y (fma.f64 y -1/8 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/2 y) (+.f64 (.f64 1/16 (pow.f64 y 3)) (*.f64 -1/8 (pow.f64 y 2)))))
(+.f64 1 (fma.f64 1/2 y (fma.f64 1/16 (pow.f64 y 3) (.f64 -1/8 (.f64 y y)))))
(+.f64 1 (fma.f64 1/2 y (fma.f64 -1/8 (.f64 y y) (.f64 1/16 (pow.f64 y 3)))))
(+.f64 1 (fma.f64 1/16 (pow.f64 y 3) (.f64 y (+.f64 1/2 (.f64 y -1/8)))))
(fma.f64 1/16 (pow.f64 y 3) (fma.f64 y (fma.f64 y -1/8 1/2) 1))
(fma.f64 y (fma.f64 y (fma.f64 y 1/16 -1/8) 1/2) 1)

localize67.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))
✓	0.0b	(+.f64 (sqrt.f64 z) (sqrt.f64 y))
✓	0.0b	(-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
✓	6.3b	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))

Compiler

Compiled 101 to 55 computations (45.5% saved)

series33.0ms (0.1%)

Counts

4 → 17

Calls

33 calls:

Time	Variable		Point	Expression
15.0ms	x	@	inf	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))
1.0ms	y	@	-inf	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
1.0ms	y	@	inf	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
1.0ms	z	@	-inf	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
1.0ms	x	@	-inf	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))

rewrite155.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

391×	`log1p-udef_binary64`
390×	`expm1-udef_binary64`
239×	`add-sqr-sqrt_binary64`
236×	`*-un-lft-identity_binary64`
236×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	95
1	452	95
2	7179	95

Stop Event

1×	node limit

Counts

4 → 177

Calls

Call 1

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

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

simplify246.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

3771×	`fma-neg_binary64`
879×	`sub-neg_binary64`
501×	`fma-def_binary64`
437×	`associate--r+_binary64`
339×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	306
1	117	306
2	275	306
3	696	306
4	2088	306
5	3554	306
6	5468	306
7	6538	306
8	7223	306
9	7332	306
10	7364	306
11	7415	306
12	7497	306
13	7497	306
14	7497	306
15	7497	306

Stop Event

1×	node limit

Counts

194 → 204

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 z)) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (sqrt.f64 z))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 z)) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(-.f64 (+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 z)))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 z)) (sqrt.f64 x)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 x) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 z)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 z)))
(-.f64 (-.f64 1 (sqrt.f64 z)) (sqrt.f64 x))
(-.f64 (-.f64 1 (sqrt.f64 x)) (sqrt.f64 z))
(*.f64 -1 (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 z)))
(-.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (sqrt.f64 z))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 z)) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(sqrt.f64 y)
(sqrt.f64 z)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))
(+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 1 (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 1 (sqrt.f64 z)) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 1 (+.f64 (sqrt.f64 y) (sqrt.f64 z))))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (sqrt.f64 z))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 z)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 z)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 1 (sqrt.f64 z)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 1 (sqrt.f64 x)) (sqrt.f64 z)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 z)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))

localize70.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 z 1))
✓	0.0b	(+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))
✓	2.8b	(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))

Compiler

Compiled 127 to 63 computations (50.4% saved)

series17.0ms (0.1%)

Counts

4 → 18

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	t	@	inf	(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
1.0ms	x	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
1.0ms	z	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
1.0ms	t	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x))))))
1.0ms	z	@	inf	(+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))

rewrite221.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

389×	`log1p-udef_binary64`
388×	`expm1-udef_binary64`
238×	`add-sqr-sqrt_binary64`
235×	`*-un-lft-identity_binary64`
235×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	85
1	451	85
2	7129	85

Stop Event

1×	node limit

Counts

4 → 148

Calls

Call 1

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

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

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

856×	`sub-neg_binary64`
801×	`fma-def_binary64`
647×	`fma-neg_binary64`
536×	`unswap-sqr_binary64`
484×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	314
1	139	312
2	339	308
3	944	302
4	2859	302
5	6251	302

Stop Event

1×	node limit

Counts

166 → 178

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(+.f64 (sqrt.f64 x) (sqrt.f64 t))
(+.f64 (sqrt.f64 z) (sqrt.f64 x))
(+.f64 (sqrt.f64 z) (sqrt.f64 t))
1
(+.f64 1 (*.f64 1/2 z))
(+.f64 1 (+.f64 (.f64 -1/8 (pow.f64 z 2)) (.f64 1/2 z)))
(+.f64 (.f64 1/16 (pow.f64 z 3)) (+.f64 1 (+.f64 (.f64 -1/8 (pow.f64 z 2)) (*.f64 1/2 z))))

Outputs
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 x)) 1))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 1 (sqrt.f64 z)) (sqrt.f64 x))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 x))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 x))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(+.f64 1 (-.f64 (-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 x)) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 t)) (sqrt.f64 x))))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 t) -1)))
(+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(-.f64 (-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 x)) (sqrt.f64 t))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 t)) (sqrt.f64 x)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t)))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 t)) (sqrt.f64 z))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 t))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 t)) (sqrt.f64 z)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
(+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 t)) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 t) -1)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 t)) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))) (sqrt.f64 t))
(+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 t)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))
(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))
(-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 t)) (sqrt.f64 z))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 z) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 x))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 x))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 x) (sqrt.f64 t))
(+.f64 (sqrt.f64 z) (sqrt.f64 x))
(+.f64 (sqrt.f64 z) (sqrt.f64 t))
1
(+.f64 1 (*.f64 1/2 z))
(+.f64 1 (*.f64 z 1/2))
(fma.f64 z 1/2 1)
(+.f64 1 (+.f64 (.f64 -1/8 (pow.f64 z 2)) (.f64 1/2 z)))
(+.f64 1 (fma.f64 -1/8 (.f64 z z) (.f64 z 1/2)))
(+.f64 (fma.f64 z 1/2 1) (.f64 z (.f64 z -1/8)))
(fma.f64 z 1/2 (fma.f64 z (*.f64 z -1/8) 1))
(fma.f64 z (fma.f64 z -1/8 1/2) 1)
(+.f64 (.f64 1/16 (pow.f64 z 3)) (+.f64 1 (+.f64 (.f64 -1/8 (pow.f64 z 2)) (*.f64 1/2 z))))
(fma.f64 1/16 (pow.f64 z 3) (+.f64 1 (fma.f64 -1/8 (.f64 z z) (.f64 z 1/2))))
(+.f64 (fma.f64 z 1/2 (.f64 z (.f64 z -1/8))) (fma.f64 1/16 (pow.f64 z 3) 1))
(fma.f64 1/16 (pow.f64 z 3) (fma.f64 z 1/2 (fma.f64 z (*.f64 z -1/8) 1)))
(fma.f64 1/16 (pow.f64 z 3) (fma.f64 z (fma.f64 z -1/8 1/2) 1))
(fma.f64 z 1/2 (fma.f64 z (*.f64 z (fma.f64 z 1/16 -1/8)) 1))

localize135.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
	0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	3.0b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 169 to 100 computations (40.8% saved)

series6.0ms (0%)

Counts

1 → 1

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

(/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

2.0ms

inf

(/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

1.0ms

(/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

rewrite85.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

942×	`pow1_binary64`
876×	`add-log-exp_binary64`
875×	`log1p-expm1-u_binary64`
875×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	244	11
2	2677	11

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

Outputs

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

simplify38.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

Counts

34 → 34

Calls

Call 1

Inputs
1

Outputs
1

localize95.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.3b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
✓	3.0b	(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 165 to 104 computations (37% saved)

series3.0ms (0%)

Counts

2 → 2

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
1.0ms	y	@	inf	(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
0.0ms	y	@	-inf	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
0.0ms	y	@	-inf	(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
0.0ms	y	@	0	(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))

rewrite118.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

870×	`pow1_binary64`
810×	`add-log-exp_binary64`
810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
790×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	176	22
2	2291	22

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))

Outputs

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

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

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	2
1	4	2

Stop Event

1×

saturated

Counts

81 → 43

Calls

Call 1

Inputs
1
1

Outputs
1
1

eval904.0ms (3.4%)

Compiler: Compiled 29944 to 18157 computations (39.4% saved)

prune360.0ms (1.4%)

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	768	20	788
Fresh	8	5	13
Picked	0	1	1
Done	3	2	5
Total	779	28	807

Error

0.6b

Counts

807 → 28

Alt Table

Click to see full alt table

Status	Error	Program
✓	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	42.5b	(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
	5.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	15.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 y 1))) 3) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	42.6b	(fma.f64 (pow.f64 (+.f64 z 1) 1/4) (pow.f64 (+.f64 z 1) 1/4) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))
▶	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
▶	38.1b	(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
✓	1.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	35.6b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
▶	6.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 (+.f64 1 y) y) (sqrt.f64 (*.f64 (+.f64 1 y) y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (/.f64 (+.f64 1 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (/.f64 y (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	43.3b	(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
✓	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	43.2b	(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (+.f64 z 1)))
	42.7b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 2)
	25.4b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
	42.7b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 3)
	41.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
	42.7b	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
	37.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	5.7b	(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
	26.3b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) 3))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	20.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	1.2b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 1741 to 1347 computations (22.6% saved)

localize134.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
✓	0.1b	(/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	0.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 220 to 125 computations (43.2% saved)

series17.0ms (0.1%)

Counts

2 → 3

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	y	@	inf	(+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
4.0ms	y	@	-inf	(/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
2.0ms	y	@	-inf	(+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
2.0ms	x	@	-inf	(+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
1.0ms	x	@	inf	(+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))

rewrite92.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

502×	`fma-neg_binary64`
305×	`expm1-udef_binary64`
305×	`log1p-udef_binary64`
199×	`add-sqr-sqrt_binary64`
196×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	44
1	485	35
2	5830	35

Stop Event

1×	node limit

Counts

2 → 104

Calls

Call 1

Inputs

(/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

(+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))

Outputs

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

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	24	35

Stop Event

1×

saturated

Counts

107 → 107

Calls

Call 1

Inputs
1
(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))

Outputs
1
(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 y))
✓	0.0b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
✓	2.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
✓	5.4b	(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))

Compiler

Compiled 55 to 30 computations (45.5% saved)

series11.0ms (0%)

Counts

4 → 13

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
1.0ms	x	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
1.0ms	y	@	-inf	(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
1.0ms	y	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
1.0ms	y	@	inf	(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))

rewrite114.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`log-prod_binary64`
617×	`fma-neg_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
220×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	301	54
2	4607	54

Stop Event

1×	node limit

Counts

4 → 209

Calls

Call 1

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

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

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-neg_binary64`
536×	`unswap-sqr_binary64`
508×	`associate-l_binary64`
492×	`fma-def_binary64`
328×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	121
1	78	119
2	153	116
3	386	109
4	944	106
5	2723	106
6	4408	106
7	5784	106
8	7171	106

Stop Event

1×	node limit

Counts

222 → 227

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 x))
(*.f64 -1 (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(sqrt.f64 y)
(sqrt.f64 x)
1
(+.f64 1 (*.f64 1/2 y))
(+.f64 1 (+.f64 (.f64 1/2 y) (.f64 -1/8 (pow.f64 y 2))))
(+.f64 1 (+.f64 (.f64 1/2 y) (+.f64 (.f64 1/16 (pow.f64 y 3)) (*.f64 -1/8 (pow.f64 y 2)))))

Outputs
(-.f64 1 (sqrt.f64 x))
(*.f64 -1 (sqrt.f64 x))
(neg.f64 (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (sqrt.f64 x)))
(+.f64 (-.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(sqrt.f64 y)
(sqrt.f64 x)
1
(+.f64 1 (*.f64 1/2 y))
(+.f64 1 (*.f64 y 1/2))
(fma.f64 y 1/2 1)
(+.f64 1 (+.f64 (.f64 1/2 y) (.f64 -1/8 (pow.f64 y 2))))
(+.f64 1 (fma.f64 1/2 y (.f64 -1/8 (.f64 y y))))
(+.f64 1 (fma.f64 y 1/2 (.f64 y (.f64 y -1/8))))
(fma.f64 y 1/2 (fma.f64 y (*.f64 y -1/8) 1))
(fma.f64 y (fma.f64 y -1/8 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/2 y) (+.f64 (.f64 1/16 (pow.f64 y 3)) (*.f64 -1/8 (pow.f64 y 2)))))
(+.f64 1 (fma.f64 1/2 y (fma.f64 1/16 (pow.f64 y 3) (.f64 -1/8 (.f64 y y)))))
(+.f64 1 (fma.f64 y 1/2 (fma.f64 -1/8 (.f64 y y) (.f64 1/16 (pow.f64 y 3)))))
(+.f64 (fma.f64 y 1/2 1) (.f64 (.f64 y y) (+.f64 -1/8 (*.f64 y 1/16))))
(fma.f64 y 1/2 (fma.f64 (*.f64 y y) (fma.f64 y 1/16 -1/8) 1))
(fma.f64 y (fma.f64 y (fma.f64 y 1/16 -1/8) 1/2) 1)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
✓	0.0b	(+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
✓	0.7b	(-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))
✓	0.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 90 to 58 computations (35.6% saved)

series14.0ms (0.1%)

Counts

4 → 10

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
1.0ms	x	@	-inf	(+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
1.0ms	t	@	-inf	(+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
1.0ms	t	@	inf	(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
1.0ms	t	@	-inf	(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))

rewrite223.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

756×	`fma-neg_binary64`
315×	`expm1-udef_binary64`
315×	`log1p-udef_binary64`
192×	`add-sqr-sqrt_binary64`
188×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	76
1	363	76
2	5808	76

Stop Event

1×	node limit

Counts

4 → 189

Calls

Call 1

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

Outputs
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(-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 3)) (/.f64 1 (+.f64 1 (.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2)) (/.f64 1 (-.f64 0 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))) (+.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 0 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))) (-.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 3)) (+.f64 1 (.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 3)) (+.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2) (-.f64 0 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2)) (-.f64 0 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 3))) (neg.f64 (+.f64 1 (.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2))) (neg.f64 (-.f64 0 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 8 (pow.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 3)) (+.f64 4 (-.f64 (pow.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 2) (.f64 2 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2) 1) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4 (pow.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 2)) (-.f64 2 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1)) 2)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t)) 1))) 1)))))

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
420×	`fma-neg_binary64`
206×	`distribute-rgt-in_binary64`
189×	`associate--r+_binary64`
164×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	114
1	50	114
2	93	114
3	178	114
4	302	114
5	489	114
6	895	114
7	1564	114
8	2177	114
9	2611	114
10	2979	114
11	3015	114

Stop Event

1×

saturated

Counts

199 → 202

Calls

Call 1

Inputs
1
1
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 3 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(-.f64 (+.f64 3 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))

Outputs
1
1
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 1 (sqrt.f64 t)))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 2 (sqrt.f64 x)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(-.f64 (+.f64 3 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(+.f64 3 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 3 (sqrt.f64 t)))
(-.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 t) 3))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 t))) (sqrt.f64 t))
(+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
(-.f64 (+.f64 3 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 3 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 3 (sqrt.f64 x)))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 3) (sqrt.f64 x))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 2 (sqrt.f64 x)))

localize222.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.0b	(-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))
	0.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 187 to 112 computations (40.1% saved)

series8.0ms (0%)

Counts

2 → 4

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
2.0ms	x	@	inf	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
1.0ms	x	@	0	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
1.0ms	y	@	-inf	(-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))
1.0ms	y	@	inf	(-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))

rewrite269.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

698×	`log-prod_binary64`
395×	`fma-neg_binary64`
272×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`
229×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	383	21
2	4739	21

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

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

Outputs

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

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	8	10

Stop Event

1×

saturated

Counts

110 → 108

Calls

Call 1

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

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

localize143.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.6b	(sqrt.f64 (*.f64 (+.f64 1 y) y))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
✓	4.2b	(-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))

Compiler

Compiled 242 to 163 computations (32.6% saved)

series28.0ms (0.1%)

Counts

2 → 20

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	y	@	-inf	(-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))
1.0ms	y	@	inf	(-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))
1.0ms	y	@	-inf	(sqrt.f64 (*.f64 (+.f64 1 y) y))
1.0ms	y	@	0	(-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))
1.0ms	y	@	0	(sqrt.f64 (*.f64 (+.f64 1 y) y))

rewrite83.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`prod-diff_binary64`
464×	`log-prod_binary64`
379×	`fma-def_binary64`
264×	`pow2_binary64`
181×	`pow-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	224	22
2	2964	19

Stop Event

1×	node limit

Counts

2 → 131

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))
(sqrt.f64 (*.f64 (+.f64 1 y) y))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 y (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 y (sqrt.f64 y)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 y (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 y (sqrt.f64 y))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 y (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 y (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 y (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y y y)) (pow.f64 (fma.f64 y y y) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 y y y) 1/6) (cbrt.f64 (fma.f64 y y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 y y y) 1/4) (pow.f64 (fma.f64 y y y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 y (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y y y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y y y) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y y y) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y y y)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y y y) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y y y) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y y y) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 y (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 y (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 y (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y y y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 y (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 y) y)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 y (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 y (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 y (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 y y y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 y (sqrt.f64 y))) 1))))))

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-l_binary64`
600×	`associate-/l*_binary64`
513×	`associate-r_binary64`
312×	`fma-def_binary64`
218×	`associate-*l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	94	470
1	258	458
2	697	369
3	2029	323
4	7529	303

Stop Event

1×	node limit

Counts

151 → 164

Calls

Call 1

Inputs
(-.f64 1 (pow.f64 y 3/2))
(-.f64 (+.f64 1 (*.f64 3/2 y)) (pow.f64 y 3/2))
(-.f64 (+.f64 1 (+.f64 (.f64 3/2 y) (.f64 3/8 (pow.f64 y 2)))) (pow.f64 y 3/2))
(-.f64 (+.f64 1 (+.f64 (.f64 3/2 y) (+.f64 (.f64 -1/16 (pow.f64 y 3)) (*.f64 3/8 (pow.f64 y 2))))) (pow.f64 y 3/2))
(*.f64 3/2 (sqrt.f64 y))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 y))) (.f64 3/2 (sqrt.f64 y)))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 y))) (+.f64 (.f64 3/2 (sqrt.f64 y)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 y))) (+.f64 (.f64 3/2 (sqrt.f64 y)) (+.f64 (.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (.f64 3/128 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))))))
(.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y))
(+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 2))) (.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y)))
(+.f64 (.f64 -1/16 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 3))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 2))) (.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y))))
(+.f64 (.f64 -1/16 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 3))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 2))) (+.f64 (.f64 3/128 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 4))) (.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y)))))
y
(+.f64 1/2 y)
(-.f64 (+.f64 1/2 y) (*.f64 1/8 (/.f64 1 y)))
(-.f64 (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 y 2))) y)) (.f64 1/8 (/.f64 1 y)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))
(+.f64 1/2 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y)))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))) (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y)) (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 y 2)))))))

Outputs
(-.f64 1 (pow.f64 y 3/2))
(-.f64 (+.f64 1 (*.f64 3/2 y)) (pow.f64 y 3/2))
(+.f64 1 (-.f64 (*.f64 y 3/2) (pow.f64 y 3/2)))
(-.f64 (fma.f64 y 3/2 1) (pow.f64 y 3/2))
(-.f64 (+.f64 1 (+.f64 (.f64 3/2 y) (.f64 3/8 (pow.f64 y 2)))) (pow.f64 y 3/2))
(+.f64 1 (-.f64 (fma.f64 3/2 y (.f64 3/8 (.f64 y y))) (pow.f64 y 3/2)))
(+.f64 1 (-.f64 (fma.f64 y 3/2 (.f64 3/8 (.f64 y y))) (pow.f64 y 3/2)))
(-.f64 (fma.f64 y 3/2 (fma.f64 3/8 (*.f64 y y) 1)) (pow.f64 y 3/2))
(fma.f64 y (+.f64 3/2 (*.f64 y 3/8)) (-.f64 1 (pow.f64 y 3/2)))
(-.f64 (+.f64 1 (+.f64 (.f64 3/2 y) (+.f64 (.f64 -1/16 (pow.f64 y 3)) (*.f64 3/8 (pow.f64 y 2))))) (pow.f64 y 3/2))
(+.f64 1 (-.f64 (fma.f64 3/2 y (fma.f64 -1/16 (pow.f64 y 3) (.f64 3/8 (.f64 y y)))) (pow.f64 y 3/2)))
(+.f64 1 (-.f64 (fma.f64 y 3/2 (fma.f64 3/8 (.f64 y y) (.f64 -1/16 (pow.f64 y 3)))) (pow.f64 y 3/2)))
(+.f64 1 (-.f64 (fma.f64 y 3/2 (.f64 (.f64 y y) (+.f64 3/8 (*.f64 y -1/16)))) (pow.f64 y 3/2)))
(+.f64 1 (-.f64 (.f64 y (+.f64 3/2 (.f64 y (+.f64 3/8 (*.f64 y -1/16))))) (pow.f64 y 3/2)))
(*.f64 3/2 (sqrt.f64 y))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 y))) (.f64 3/2 (sqrt.f64 y)))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 y)) (*.f64 3/2 (sqrt.f64 y)))
(fma.f64 3/2 (sqrt.f64 y) (*.f64 3/8 (sqrt.f64 (/.f64 1 y))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 y))) (+.f64 (.f64 3/2 (sqrt.f64 y)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 y)) (fma.f64 3/2 (sqrt.f64 y) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))
(fma.f64 3/2 (sqrt.f64 y) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 3/8 (sqrt.f64 (/.f64 1 y)))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 y))) (+.f64 (.f64 3/2 (sqrt.f64 y)) (+.f64 (.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3)))) (.f64 3/128 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 y)) (fma.f64 3/2 (sqrt.f64 y) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 3/128 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))))))
(fma.f64 3/2 (sqrt.f64 y) (fma.f64 3/8 (sqrt.f64 (/.f64 1 y)) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 3/128 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 y)) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (fma.f64 3/128 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (*.f64 3/2 (sqrt.f64 y)))))
(.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y))
(/.f64 (*.f64 3/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))) y)
(*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y))
(.f64 (/.f64 3/2 y) (.f64 (pow.f64 (/.f64 -1 y) -3/2) (pow.f64 -1 3/2)))
(*.f64 (pow.f64 (exp.f64 3/2) (log.f64 y)) (/.f64 3/2 y))
(*.f64 (pow.f64 y 3/2) (/.f64 3/2 y))
(+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 2))) (.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y)))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (.f64 y y)) (/.f64 (.f64 3/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))) y))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) (.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (.f64 y y))))
(.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 y) -3/2) (pow.f64 -1 3/2)) y) (+.f64 3/2 (/.f64 3/8 y)))
(*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 y)) y) (+.f64 3/2 (/.f64 3/8 y)))
(*.f64 (/.f64 (pow.f64 y 3/2) y) (+.f64 3/2 (/.f64 3/8 y)))
(+.f64 (.f64 -1/16 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 3))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 2))) (.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y))))
(fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (pow.f64 y 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (.f64 y y)) (/.f64 (.f64 3/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))) y)))
(fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (pow.f64 y 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) (.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (.f64 y y)))))
(fma.f64 3/2 (/.f64 (.f64 (pow.f64 (/.f64 -1 y) -3/2) (pow.f64 -1 3/2)) y) (.f64 (/.f64 (pow.f64 (/.f64 -1 y) -3/2) (/.f64 (*.f64 y y) (pow.f64 -1 3/2))) (+.f64 3/8 (/.f64 -1/16 y))))
(.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 y)) y) (+.f64 3/2 (+.f64 (/.f64 3/8 y) (/.f64 -1/16 (.f64 y y)))))
(.f64 (/.f64 (pow.f64 y 3/2) y) (+.f64 3/2 (+.f64 (/.f64 3/8 y) (/.f64 -1/16 (.f64 y y)))))
(+.f64 (.f64 -1/16 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 3))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 2))) (+.f64 (.f64 3/128 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (pow.f64 y 4))) (.f64 3/2 (/.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) y)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (pow.f64 y 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (.f64 y y)) (fma.f64 3/128 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1))) (pow.f64 y 4)) (/.f64 (.f64 3/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))) y))))
(fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (pow.f64 y 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (.f64 y y)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) (.f64 3/128 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (pow.f64 y 4))))))
(+.f64 (.f64 (/.f64 (pow.f64 (/.f64 -1 y) -3/2) (/.f64 (.f64 y y) (pow.f64 -1 3/2))) (+.f64 3/8 (/.f64 3/128 (.f64 y y)))) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 y) -3/2) (pow.f64 -1 3/2)) y) (+.f64 3/2 (/.f64 -1/16 (.f64 y y)))))
(+.f64 (.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 y)) y) (+.f64 3/2 (/.f64 3/8 y))) (.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 y)) (pow.f64 y 3)) (+.f64 -1/16 (/.f64 3/128 y))))
(+.f64 (.f64 (/.f64 (pow.f64 y 3/2) y) (+.f64 3/2 (/.f64 3/8 y))) (.f64 (/.f64 (pow.f64 y 3/2) (pow.f64 y 3)) (+.f64 -1/16 (/.f64 3/128 y))))
y
(+.f64 1/2 y)
(+.f64 y 1/2)
(-.f64 (+.f64 1/2 y) (*.f64 1/8 (/.f64 1 y)))
(+.f64 1/2 (-.f64 y (/.f64 1/8 y)))
(+.f64 1/2 (+.f64 y (/.f64 -1/8 y)))
(-.f64 (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 y 2))) y)) (.f64 1/8 (/.f64 1 y)))
(+.f64 1/2 (-.f64 (+.f64 y (/.f64 1/16 (*.f64 y y))) (/.f64 1/8 y)))
(+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 y y))) (+.f64 y (/.f64 -1/8 y)))
(+.f64 y (+.f64 (/.f64 -1/8 y) (+.f64 1/2 (/.f64 (/.f64 1/16 y) y))))
(+.f64 (-.f64 y (/.f64 1/8 y)) (+.f64 1/2 (/.f64 1/16 (*.f64 y y))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))
y
(+.f64 1/2 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y)))
(+.f64 y 1/2)
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))) (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))))
(+.f64 1/2 (-.f64 y (/.f64 1/8 y)))
(+.f64 1/2 (+.f64 y (/.f64 -1/8 y)))
(+.f64 1/2 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y))) (+.f64 (.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) y)) (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 y 2)))))))
(+.f64 1/2 (-.f64 (+.f64 y (/.f64 1/16 (*.f64 y y))) (/.f64 1/8 y)))
(+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 y y))) (+.f64 y (/.f64 -1/8 y)))
(+.f64 y (+.f64 (/.f64 -1/8 y) (+.f64 1/2 (/.f64 (/.f64 1/16 y) y))))
(+.f64 (-.f64 y (/.f64 1/8 y)) (+.f64 1/2 (/.f64 1/16 (*.f64 y y))))

eval1.1s (4.2%)

Compiler: Compiled 40029 to 25667 computations (35.9% saved)

prune246.0ms (0.9%)

Pruning

42 alts after pruning (39 fresh and 3 done)

	Pruned	Kept	Total
New	1006	27	1033
Fresh	8	12	20
Picked	1	0	1
Done	4	3	7
Total	1019	42	1061

Error

0.6b

Counts

1061 → 42

Alt Table

Click to see full alt table

Status	Error	Program
	39.3b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
	42.5b	(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
	5.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	37.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
✓	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
✓	1.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	41.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	20.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (*.f64 1/2 y) (sqrt.f64 y)) 1)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
▶	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
	58.0b	(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 3)))
	6.2b	(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	37.8b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
	22.0b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (log.f64 (/.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 y 1))) (exp.f64 (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	43.2b	(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (+.f64 z 1)))
	25.4b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
	35.9b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
	29.9b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
	30.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
	23.4b	(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	42.7b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 3)
	42.7b	(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
▶	1.2b	(+.f64 (+.f64 (/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	20.4b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	35.6b	(+.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
	37.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	38.1b	(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	34.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 y))) 3) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	5.7b	(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
	38.0b	(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
	37.7b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
▶	26.3b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
✓	1.2b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	23.6b	(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
▶	36.2b	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
	21.7b	(+.f64 (+.f64 (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (-.f64 (+.f64 1 (.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	35.6b	(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))

Compiler

Compiled 2225 to 1723 computations (22.6% saved)

localize87.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (sqrt.f64 y))
✓	0.1b	(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))
	0.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.8b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 214 to 111 computations (48.1% saved)

series47.0ms (0.2%)

Counts

2 → 3

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	x	@	-inf	(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))
11.0ms	y	@	-inf	(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))
9.0ms	y	@	inf	(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))
6.0ms	x	@	inf	(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))
3.0ms	y	@	0	(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))

rewrite92.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

881×	`fma-def_binary64`
461×	`fma-neg_binary64`
264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
236×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	300	56
2	4892	56

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

Inputs

(/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))

(hypot.f64 1 (sqrt.f64 y))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) 2)) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 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simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
6×	`associate-+r+_binary64`
6×	`associate-+l+_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	55
1	29	55
2	43	55
3	47	55

Stop Event

1×

saturated

Counts

64 → 65

Calls

Call 1

Inputs

(/.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

(/.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

Outputs
(/.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
(/.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(/.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
1

localize12.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 22 to 15 computations (31.8% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
✓	0.0b	(+.f64 (sqrt.f64 y) (sqrt.f64 z))
✓	0.1b	(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))
✓	5.4b	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))))

Compiler

Compiled 72 to 40 computations (44.4% saved)

series15.0ms (0.1%)

Counts

4 → 13

Calls

24 calls:

Time	Variable		Point	Expression
4.0ms	z	@	inf	(+.f64 (sqrt.f64 y) (sqrt.f64 z))
1.0ms	z	@	-inf	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
1.0ms	y	@	-inf	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
1.0ms	y	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))))
1.0ms	z	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))))

rewrite131.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`fma-neg_binary64`
286×	`expm1-udef_binary64`
286×	`log1p-udef_binary64`
240×	`log-pow_binary64`
220×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	331	75
2	5184	75

Stop Event

1×	node limit

Counts

4 → 229

Calls

Call 1

Inputs
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))
(+.f64 (sqrt.f64 y) (sqrt.f64 z))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))

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

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-def_binary64`
332×	`fma-neg_binary64`
134×	`cancel-sign-sub-inv_binary64`
103×	`associate--r+_binary64`
100×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	134
1	46	134
2	73	134
3	135	134
4	220	134
5	371	134
6	689	134
7	982	134
8	1383	134
9	1711	134
10	1963	134
11	1983	134

Stop Event

1×

saturated

Counts

242 → 244

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))
(-.f64 1 (sqrt.f64 z))
(*.f64 -1 (sqrt.f64 z))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(sqrt.f64 z)
(sqrt.f64 y)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))

Outputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z)))
(-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))
(-.f64 1 (sqrt.f64 z))
(*.f64 -1 (sqrt.f64 z))
(neg.f64 (sqrt.f64 z))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(sqrt.f64 z)
(sqrt.f64 y)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 2 (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z)))

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
✓	0.1b	(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
✓	2.3b	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
	5.4b	(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))

Compiler

Compiled 80 to 43 computations (46.3% saved)

series5.0ms (0%)

Counts

2 → 7

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
0.0ms	x	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
0.0ms	y	@	0	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
0.0ms	y	@	inf	(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
0.0ms	y	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))

rewrite105.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`log-prod_binary64`
591×	`fma-neg_binary64`
270×	`expm1-udef_binary64`
270×	`log1p-udef_binary64`
234×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	323	40
2	4759	40

Stop Event

1×	node limit

Counts

2 → 124

Calls

Call 1

Inputs
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))

Outputs

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

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

226×	`fma-def_binary64`
198×	`fma-neg_binary64`
82×	`cancel-sign-sub-inv_binary64`
60×	`distribute-rgt-in_binary64`
60×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	72
1	35	72
2	50	72
3	88	72
4	138	72
5	229	72
6	422	72
7	594	72
8	831	72
9	1031	72
10	1183	72
11	1195	72

Stop Event

1×

saturated

Counts

131 → 133

Calls

Call 1

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

Outputs
(-.f64 1 (sqrt.f64 x))
(*.f64 -1 (sqrt.f64 x))
(neg.f64 (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (sqrt.f64 x)))
(+.f64 (-.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
✓	0.1b	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
✓	0.6b	(cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x)))))
✓	5.6b	(-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))

Compiler

Compiled 87 to 44 computations (49.4% saved)

series80.0ms (0.3%)

Counts

3 → 9

Calls

18 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	(cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x)))))
10.0ms	x	@	inf	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
9.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
7.0ms	y	@	inf	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
7.0ms	x	@	inf	(-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))

rewrite130.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`log-prod_binary64`
532×	`fma-neg_binary64`
269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
229×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	343	74
2	4691	74

Stop Event

1×	node limit

Counts

3 → 194

Calls

Call 1

Inputs

(-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))

(cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x)))))

(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 y)) (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 y)) (*.f64 (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (fma.f64 (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) 1 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (fma.f64 (neg.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) 2)) (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (+.f64 (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (+.f64 1 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 1) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) 1/6) (*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) 1/6) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) 3)) (/.f64 1 (+.f64 (+.f64 1 y) (*.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) (+.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (-.f64 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(sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 y)) (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 y)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 y)) 1/2) (neg.f64 (+.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (+.f64 1 y) 1/4) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (-.f64 (pow.f64 (+.f64 1 y) 1/4) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))))

simplify185.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1011×	`sqr-pow_binary64`
546×	`cube-prod_binary64`
487×	`fabs-mul_binary64`
459×	`associate-l_binary64`
390×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	123
1	58	123
2	109	123
3	209	123
4	407	123
5	814	123
6	2161	123
7	2551	123
8	2881	123
9	3228	123
10	3627	123
11	4211	123
12	5022	123
13	5581	123
14	6103	123
15	6459	123
16	6819	123
17	7027	123

Stop Event

1×	node limit

Counts

203 → 130

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1/3)
(pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1/3)
(pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3)
(*.f64 (pow.f64 1 1/3) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 1 1/3))
(*.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) (pow.f64 1 1/3))

Outputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 y) 1))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) -1))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 1 (sqrt.f64 y)))
(pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)) 1/3)
(cbrt.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (sqrt.f64 x))))
(pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1/3)
(cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3)
(cbrt.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 y) 1)))
(cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) -1)))
(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 1 (sqrt.f64 y))))
(*.f64 (pow.f64 1 1/3) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 1 1/3))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(*.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) (pow.f64 1 1/3))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 y) 1))
(-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) -1))
(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 1 (sqrt.f64 y)))

eval463.0ms (1.7%)

Compiler: Compiled 26303 to 16051 computations (39% saved)

prune209.0ms (0.8%)

Pruning

57 alts after pruning (54 fresh and 3 done)

	Pruned	Kept	Total
New	840	34	874
Fresh	14	20	34
Picked	1	0	1
Done	4	3	7
Total	859	57	916

Error

0.6b

Counts

916 → 57

Alt Table

Click to see full alt table

Status	Error	Program
	5.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	37.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
	35.6b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
	23.9b	(pow.f64 (cbrt.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))) 3)
✓	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
✓	41.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	20.7b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (*.f64 1/2 y) (sqrt.f64 y)) 1)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	35.7b	(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x)))))
	24.2b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 3) 3)
	5.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	58.0b	(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
	36.4b	(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
	22.0b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (log.f64 (/.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 y 1))) (exp.f64 (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	1.2b	(+.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.2b	(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	24.3b	(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 2) 3) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))) 3)
	42.7b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 2)
	42.6b	(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	42.7b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 3)
	25.4b	(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
	43.2b	(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (+.f64 z 1)))
	25.4b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
	29.9b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
	33.9b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
	38.2b	(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
	30.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
	2.1b	(+.f64 (+.f64 (/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (.f64 (+.f64 (exp.f64 (.f64 1/2 (log1p.f64 y))) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	23.4b	(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	1.5b	(+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) 3) 1/3) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	25.4b	(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
	41.8b	1
	23.7b	(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
	43.0b	(/.f64 (-.f64 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 1 (sqrt.f64 (+.f64 1 z)))) (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 2)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	20.4b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	24.3b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
	41.2b	(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
	41.2b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
	37.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	25.4b	(+.f64 1 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
	21.7b	(+.f64 (+.f64 (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (-.f64 (+.f64 1 (.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	43.2b	(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
	37.1b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	34.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
	24.3b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 2) (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))) 3)
	38.1b	(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	35.9b	(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x))))) 2)
	23.4b	(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
	23.6b	(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	38.4b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
	36.0b	(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
	35.9b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
	38.0b	(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
	37.7b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
✓	1.2b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.5b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	1.2b	(+.f64 (+.f64 (.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (.f64 (+.f64 1 x) x)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 1613 to 1257 computations (22.1% saved)

regimes914.0ms (3.4%)

Counts

101 → 1

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(pow.f64 (cbrt.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))) 3)
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x))))) 2)
(+.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 3)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 y))) 3) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 3)
(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (*.f64 1/2 y) (sqrt.f64 y)) 1)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 3) 3)
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 3)
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (-.f64 (sqrt.f64 t) (hypot.f64 1 (sqrt.f64 t)))))
(fma.f64 (pow.f64 (+.f64 z 1) 1/4) (pow.f64 (+.f64 z 1) 1/4) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 (+.f64 1 y) y) (sqrt.f64 (*.f64 (+.f64 1 y) y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) 3))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 y 1))) 3) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(/.f64 (-.f64 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 1 (sqrt.f64 (+.f64 1 z)))) (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 2)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (/.f64 (+.f64 1 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (/.f64 y (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (log.f64 (/.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 y 1))) (exp.f64 (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 y) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (.f64 (+.f64 1 x) x)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 2) (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))) 3)
(+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) 3) 1/3) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 2) 3) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))) 3)
(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (+.f64 z 1)))
(+.f64 (+.f64 (/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (/.f64 (+.f64 (+.f64 (hypot.f64 1 (sqrt.f64 y)) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (.f64 (+.f64 (exp.f64 (.f64 1/2 (log1p.f64 y))) (sqrt.f64 y)) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (-.f64 (+.f64 1 (.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Outputs

(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Calls

16 calls:

89.0ms	z
86.0ms	y
82.0ms	t
82.0ms	(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
81.0ms	x

Results

Error	Segments	Branch
1.2b	1	`x`
1.2b	1	`y`
1.2b	1	`z`
1.2b	1	`t`
1.2b	1	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.2b	1	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.2b	1	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.2b	1	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.2b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.2b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.2b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.2b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.2b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
1.2b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
1.2b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
1.2b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 2752 to 1767 computations (35.8% saved)

regimes516.0ms (1.9%)

Counts

81 → 1

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(pow.f64 (cbrt.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))) 3)
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x))))) 2)
(+.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 3)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 y))) 3) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 3)
(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (*.f64 1/2 y) (sqrt.f64 y)) 1)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 3) 3)
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 3)
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (-.f64 (sqrt.f64 t) (hypot.f64 1 (sqrt.f64 t)))))
(fma.f64 (pow.f64 (+.f64 z 1) 1/4) (pow.f64 (+.f64 z 1) 1/4) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))

Outputs

(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Calls

15 calls:

49.0ms	x
47.0ms	t
47.0ms	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
45.0ms	z
43.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Results

Error	Segments	Branch
1.7b	1	`x`
1.7b	1	`y`
1.7b	1	`z`
1.7b	1	`t`
1.7b	1	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.7b	1	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.7b	1	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.7b	1	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.7b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.7b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.7b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.7b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.7b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
1.7b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
1.7b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1867 to 1210 computations (35.2% saved)

regimes629.0ms (2.4%)

Counts

78 → 2

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(pow.f64 (cbrt.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))) 3)
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x))))) 2)
(+.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 3)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 y))) 3) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 3)
(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (*.f64 1/2 y) (sqrt.f64 y)) 1)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 3) 3)
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 3)
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (-.f64 (sqrt.f64 t) (hypot.f64 1 (sqrt.f64 t)))))
(fma.f64 (pow.f64 (+.f64 z 1) 1/4) (pow.f64 (+.f64 z 1) 1/4) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Outputs

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

(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Calls

16 calls:

108.0ms	x
81.0ms	y
77.0ms	t
43.0ms	z
30.0ms	(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))

Results

Error	Segments	Branch
1.3b	2	`x`
1.3b	2	`y`
5.1b	1	`z`
5.1b	1	`t`
1.3b	2	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.3b	2	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.3b	2	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.3b	2	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.3b	2	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.3b	2	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.3b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.3b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.4b	2	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
1.4b	2	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
5.1b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
5.1b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1767 to 1152 computations (34.8% saved)

bsearch2.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.009098181008575068	0.9881001623206763

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes595.0ms (2.2%)

Counts

77 → 2

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(pow.f64 (cbrt.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))) 3)
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x))))) 2)
(+.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 3)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 y))) 3) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 3)
(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (hypot.f64 1 (sqrt.f64 x))))) 3)
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (*.f64 1/2 y) (sqrt.f64 y)) 1)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (*.f64 1/2 y)) (sqrt.f64 y))) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 3) 3)
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))) 3)
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (-.f64 (sqrt.f64 t) (hypot.f64 1 (sqrt.f64 t)))))
(fma.f64 (pow.f64 (+.f64 z 1) 1/4) (pow.f64 (+.f64 z 1) 1/4) (-.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (+.f64 (sqrt.f64 t) (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 t))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Outputs

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

(+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Calls

15 calls:

85.0ms	x
67.0ms	y
38.0ms	t
38.0ms	z
34.0ms	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))

Results

Error	Segments	Branch
1.7b	2	`x`
1.6b	2	`y`
5.7b	1	`z`
5.7b	1	`t`
1.6b	2	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.6b	2	`(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))`
1.6b	2	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.6b	2	`(+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))`
1.6b	2	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.6b	2	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.7b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.7b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.7b	2	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
5.7b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
5.7b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1719 to 1120 computations (34.8% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9999999999999659	0.9999999999999984

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes1.1s (4.1%)

Counts

60 → 3

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(pow.f64 (cbrt.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 x)))) 3)
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x))))) 2)
(+.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) 3)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 y))) 3) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 2)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z))) 1))) 3)
(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 (+.f64 1 x)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 y)) (sqrt.f64 (+.f64 z 1))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 y)) (sqrt.f64 z)))
(+.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (neg.f64 (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 z 1)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))))))
(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))))))

Outputs

(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)

(+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))

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

Calls

12 calls:

272.0ms	x
230.0ms	z
189.0ms	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
114.0ms	y
109.0ms	t

Results

Error	Segments	Branch
12.9b	5	`x`
5.5b	3	`y`
6.7b	3	`z`
14.8b	3	`t`
5.6b	3	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
5.6b	3	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
18.8b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
18.8b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
5.5b	3	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
5.5b	3	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
19.8b	2	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`
19.8b	2	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1128 to 740 computations (34.4% saved)

bsearch375.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
142.0ms	7.711881075993128e+19	1.3739842773606532e+24
233.0ms	4.316721516833901e-34	5.515138938261204e-34

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes646.0ms (2.4%)

Counts

40 → 3

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 z)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 y) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (.f64 3 (.f64 1/3 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 z) (sqrt.f64 t)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 t))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (-.f64 z y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))))))
(+.f64 1 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(-.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 1 y) 3/2)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (/.f64 (+.f64 (pow.f64 y 3/2) (pow.f64 z 3/2)) (-.f64 (+.f64 y z) (sqrt.f64 (*.f64 y z)))))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))))

Outputs

(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)

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

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

Calls

4 calls:

218.0ms	t
179.0ms	x
108.0ms	y
79.0ms	z

Results

Error	Segments	Branch
12.9b	5	`x`
5.5b	3	`y`
6.7b	3	`z`
14.8b	3	`t`

Compiler

Compiled 597 to 393 computations (34.2% saved)

bsearch519.0ms (1.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
423.0ms	7.711881075993128e+19	1.3739842773606532e+24
96.0ms	4.316721516833901e-34	5.515138938261204e-34

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes321.0ms (1.2%)

Counts

21 → 3

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
(-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y))

Outputs

(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)

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

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

Calls

4 calls:

175.0ms	y
65.0ms	x
43.0ms	z
30.0ms	t

Results

Error	Segments	Branch
13.1b	5	`x`
5.5b	3	`y`
7.4b	3	`z`
15.5b	3	`t`

Compiler

Compiled 252 to 177 computations (29.8% saved)

bsearch508.0ms (1.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
262.0ms	7.711881075993128e+19	1.3739842773606532e+24
246.0ms	4.316721516833901e-34	5.515138938261204e-34

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes544.0ms (2%)

Counts

20 → 3

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (+.f64 1 (*.f64 1/2 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)

Outputs
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Calls

4 calls:

227.0ms	x
96.0ms	y
32.0ms	t
28.0ms	z

Results

Error	Segments	Branch
13.1b	5	`x`
5.7b	3	`y`
7.4b	3	`z`
15.5b	3	`t`

Compiler

Compiled 237 to 168 computations (29.1% saved)

bsearch663.0ms (2.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
309.0ms	619624107024.4884	14764455832178.844
353.0ms	4.316721516833901e-34	5.515138938261204e-34

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes163.0ms (0.6%)

Counts

11 → 3

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))

Outputs
(+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

Calls

4 calls:

74.0ms	x
48.0ms	t
23.0ms	z
14.0ms	y

Results

Error	Segments	Branch
17.7b	4	`x`
10.4b	2	`y`
7.4b	3	`z`
15.5b	3	`t`

Compiler

Compiled 115 to 85 computations (26.1% saved)

bsearch320.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
116.0ms	13573916016366.348	6913145637447076.0
203.0ms	4.7941979504710795e-28	6.038354685593533e-28

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes69.0ms (0.3%)

Counts

10 → 2

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 t) -3))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

Outputs
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

Calls

4 calls:

21.0ms	x
18.0ms	t
13.0ms	z
12.0ms	y

Results

Error	Segments	Branch
17.7b	4	`x`
10.4b	2	`y`
10.3b	2	`z`
15.5b	3	`t`

Compiler

Compiled 104 to 77 computations (26% saved)

bsearch124.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
123.0ms	13573916016366.348	6913145637447076.0

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes86.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

Inputs
1
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))

Outputs
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2)
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Calls

4 calls:

52.0ms	z
18.0ms	x
10.0ms	y
4.0ms	t

Results

Error	Segments	Branch
21.1b	4	`x`
12.8b	2	`y`
20.8b	4	`z`
24.3b	1	`t`

Compiler

Compiled 50 to 39 computations (22% saved)

bsearch121.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
120.0ms	0.014271528232429635	1.4073961927859935

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes23.0ms (0.1%)

Accuracy

Total -0.8b remaining (-2%)

Threshold costs -0.8b (-2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

11.0ms	t
3.0ms	y
3.0ms	x
3.0ms	z

Results

Error	Segments	Branch
41.2b	1	`x`
41.2b	1	`y`
41.2b	1	`z`
41.2b	1	`t`

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

46×	`+-commutative_binary64`
20×	`sub-neg_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	748
1	156	748
2	182	748
3	198	748
4	205	748

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(if (<=.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) 5764607523034235/576460752303423488) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))))
(if (<=.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 2251799813685203/2251799813685248) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (+.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))))
(if (<=.f64 y 1261779112950857/2923003274661805836407369665432566039311865085952) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (if (<=.f64 y 77118810759931281408) (+.f64 (sqrt.f64 (+.f64 1 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
(if (<=.f64 y 1261779112950857/2923003274661805836407369665432566039311865085952) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (if (<=.f64 y 77118810759931281408) (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
(if (<=.f64 y 1261779112950857/2923003274661805836407369665432566039311865085952) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (if (<=.f64 y 77118810759931281408) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x))) (sqrt.f64 y)) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
(if (<=.f64 y 1261779112950857/2923003274661805836407369665432566039311865085952) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (if (<=.f64 y 5075960684744609/8192) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
(if (<=.f64 z 668213668279833/1393796574908163946345982392040522594123776) (+.f64 1 (+.f64 2 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))) (if (<=.f64 z 3474922500189785/256) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(if (<=.f64 z 3474922500189785/256) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 y 8226975901385935/576460752303423488) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
1

Outputs
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
(if (<=.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) 5764607523034235/576460752303423488) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))))
(if (<=.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 5764607523034235/576460752303423488) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
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(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
1

Compiler

Compiled 529 to 398 computations (24.8% saved)

soundness0.0ms (0%)

end347.0ms (1.3%)

Compiler: Compiled 575 to 379 computations (34.1% saved)