Details

analyze317.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	74.9%	25.1%	6
0%	56.1%	43.9%	7
0%	42.1%	57.9%	8
0.4%	31.2%	68.4%	9
0.6%	25.7%	73.7%	10
0.9%	21.1%	78.1%	11
1.3%	17%	81.7%	12

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample8.5s (40.9%)

Results

4.6s	16136×	body	256	invalid
2.1s	4473×	body	512	valid
1.2s	1829×	body	1024	valid
496.0ms	1954×	body	256	valid

preprocess77.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	350
1	141	350
2	539	350
3	2848	350
4	4688	350
5	7018	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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (sqrt.f64 (+.f64 1 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 (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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (sqrt.f64 (+.f64 1 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 (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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (sqrt.f64 (+.f64 1 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 (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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (sqrt.f64 (+.f64 1 t)))))
(+.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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (sqrt.f64 (+.f64 1 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 (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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (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 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 1 y)) (sqrt.f64 y)) (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.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 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z))))))
(+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))) (-.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 t)) (sqrt.f64 (+.f64 1 t)))))

Symmetry

(sort x y z t)

Compiler

Compiled 39 to 31 computations (20.5% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
653×	`distribute-neg-in_binary64`
541×	`cancel-sign-sub-inv_binary64`
531×	`associate-+r-_binary64`
502×	`associate-+l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	54	50
2	168	50
3	975	50
4	4902	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 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))))
(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (sqrt.f64 y) (-.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))
(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 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

4.7b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	4.7b	(+.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)))
▶	56.4b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))

Status

Error

Program

▶

4.7b

(+.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)))

▶

56.4b

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

Compiler

Compiled 70 to 54 computations (22.9% saved)

localize82.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
✓	0.4b	(-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
✓	4.1b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
✓	4.4b	(-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))
✓	9.3b	(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 151 to 90 computations (40.4% saved)

series22.0ms (0.1%)

Counts

4 → 14

Calls

24 calls:

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

rewrite74.0ms (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	96
1	603	96

Stop Event

1×	node limit

Counts

4 → 141

Calls

Call 1

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

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

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
627×	`associate--r+_binary64`
571×	`sub-neg_binary64`
504×	`fma-def_binary64`
417×	`associate--l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	360
1	172	360
2	565	360
3	2401	360
4	3820	360
5	4453	360
6	5953	360

Stop Event

1×	node limit

Counts

155 → 164

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

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

localize93.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 z 1))
	0.0b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
	0.0b	(sqrt.f64 (+.f64 y 1))
	0.0b	(+.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)))
✓	0.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	4.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	4.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 142 to 87 computations (38.7% saved)

series8.0ms (0%)

Counts

4 → 4

Calls

12 calls:

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

rewrite94.0ms (0.5%)

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	7294	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 t 1)) (sqrt.f64 t))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Outputs
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simplify32.0ms (0.2%)

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

eval227.0ms (1.1%)

Compiler: Compiled 12920 to 8289 computations (35.8% saved)

prune68.0ms (0.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	301	12	313
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	302	13	315

Error

1.4b

Counts

315 → 13

Alt Table

Click to see full alt table

Status	Error	Program
▶	2.8b	(+.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)))
▶	56.4b	(*.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))))
	37.4b	(+.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)))
✓	4.7b	(+.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)))
	41.7b	(-.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))))
	3.8b	(+.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)))
▶	40.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))))
	4.4b	(+.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))))
	4.2b	(+.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)))
▶	56.4b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	24.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 x)) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))))
	5.9b	(+.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)))
▶	38.8b	(+.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))

Compiler

Compiled 869 to 669 computations (23% saved)

localize81.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 y 1))
	0.0b	(+.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)))
	0.0b	(+.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)))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.0b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	4.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	4.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 181 to 106 computations (41.4% saved)

series7.0ms (0%)

Counts

1 → 1

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

rewrite88.0ms (0.4%)

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	243	11
2	2659	11

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

Outputs

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

simplify7.0ms (0%)

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

localize37.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	2.1b	(+.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 y)))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(+.f64 (sqrt.f64 y) (sqrt.f64 t))
✓	0.0b	(sqrt.f64 (+.f64 1 y))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 y)))
✓	2.1b	(+.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))
✓	5.4b	(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t))))

Compiler

Compiled 93 to 48 computations (48.4% saved)

series15.0ms (0.1%)

Counts

4 → 22

Calls

27 calls:

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

rewrite124.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

390×	`expm1-udef_binary64`
390×	`log1p-udef_binary64`
237×	`add-sqr-sqrt_binary64`
234×	`*-un-lft-identity_binary64`
234×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	78
1	450	78
2	7159	78

Stop Event

1×	node limit

Counts

4 → 161

Calls

Call 1

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

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

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

902×	`sub-neg_binary64`
817×	`fma-def_binary64`
803×	`fma-neg_binary64`
530×	`unswap-sqr_binary64`
384×	`+-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	393
1	215	385
2	548	382
3	1610	363
4	3843	363
5	6103	363

Stop Event

1×	node limit

Counts

183 → 203

Calls

Call 1

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

localize39.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	4.7b	(-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z)))
	3.5b	(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))))
✓	0.0b	(sqrt.f64 (+.f64 1 z))
✓	3.5b	(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
✓	4.7b	(-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z)))

Compiler

Compiled 101 to 55 computations (45.5% saved)

series23.0ms (0.1%)

Counts

4 → 16

Calls

24 calls:

Time	Variable		Point	Expression
10.0ms	z	@	0	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))))
1.0ms	z	@	inf	(-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z)))
1.0ms	z	@	-inf	(-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z)))
1.0ms	t	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t)))))
1.0ms	t	@	-inf	(-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z))) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))

rewrite117.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

392×	`expm1-udef_binary64`
392×	`log1p-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	83
1	451	83
2	7164	83

Stop Event

1×	node limit

Counts

4 → 151

Calls

Call 1

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

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

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	291
1	140	289
2	339	285
3	937	279
4	2845	279
5	6045	279

Stop Event

1×	node limit

Counts

167 → 177

Calls

Call 1

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

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

localize51.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1 z)))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
	0.0b	(sqrt.f64 (+.f64 1 z))
✓	4.1b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	4.4b	(-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))
✓	9.5b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))

Compiler

Compiled 112 to 71 computations (36.6% saved)

series7.0ms (0%)

Counts

2 → 8

Calls

12 calls:

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

rewrite105.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

420×	`log1p-udef_binary64`
256×	`add-sqr-sqrt_binary64`
253×	`*-un-lft-identity_binary64`
253×	`pow1_binary64`
237×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	482	54
2	7743	54

Stop Event

1×	node limit

Counts

2 → 89

Calls

Call 1

Inputs

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

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

Outputs

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

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
575×	`associate--r+_binary64`
560×	`sub-neg_binary64`
526×	`fma-neg_binary64`
452×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	164
1	94	164
2	273	164
3	918	164
4	2918	164
5	4671	164
6	6701	164
7	7741	164

Stop Event

1×	node limit

Counts

97 → 103

Calls

Call 1

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

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

localize75.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
	0.0b	(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(sqrt.f64 (+.f64 1 y))
✓	0.0b	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
✓	0.4b	(-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
	4.4b	(-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))
✓	4.6b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))))

Compiler

Compiled 190 to 113 computations (40.5% saved)

series34.0ms (0.2%)

Counts

3 → 15

Calls

27 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
1.0ms	x	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))))
1.0ms	z	@	-inf	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))))
1.0ms	y	@	-inf	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
1.0ms	x	@	-inf	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))

rewrite91.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

319×	`add-sqr-sqrt_binary64`
316×	`*-un-lft-identity_binary64`
316×	`pow1_binary64`
295×	`add-cbrt-cube_binary64`
295×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	95
1	601	95

Stop Event

1×	node limit

Counts

3 → 115

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

839×	`sub-neg_binary64`
546×	`associate--l+_binary64`
505×	`distribute-neg-in_binary64`
432×	`associate--r-_binary64`
401×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	457
1	203	457
2	734	457
3	3074	457
4	4145	457
5	4961	457
6	7536	457

Stop Event

1×	node limit

Counts

130 → 144

Calls

Call 1

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

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

eval864.0ms (4.2%)

Compiler: Compiled 33403 to 20645 computations (38.2% saved)

prune247.0ms (1.2%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	858	20	878
Fresh	4	3	7
Picked	1	0	1
Done	3	2	5
Total	866	25	891

Error

0.6b

Counts

891 → 25

Alt Table

Click to see full alt table

Status	Error	Program
	38.7b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
	56.4b	(exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))))
	40.1b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (sqrt.f64 t))))
	39.0b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 y)))) 2) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))
	2.9b	(+.f64 (+.f64 (+.f64 (.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)))) (-.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)))
	39.3b	(+.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 y)))) 3) (-.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))
	35.5b	(-.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 y))))
✓	4.7b	(+.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)))
▶	35.5b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
	3.8b	(+.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)))
▶	24.5b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	5.4b	(-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))
▶	56.4b	(*.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) -1) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))))
	56.5b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (+.f64 2 (sqrt.f64 (+.f64 1 t))))
	56.2b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (+.f64 1 (*.f64 1/2 z))) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	56.5b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 -1 (sqrt.f64 t))))
▶	1.3b	(+.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)))
	4.4b	(+.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))))
	56.4b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))) 2)
✓	2.8b	(+.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)))
	41.7b	(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 z)))) (+.f64 (sqrt.f64 z) (sqrt.f64 y)))
	4.2b	(+.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)))
▶	56.4b	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))
	56.5b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))) 3)
	56.5b	(expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))))

Compiler

Compiled 1470 to 1154 computations (21.5% saved)

localize105.0ms (0.5%)

Local error

Found 8 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))))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(+.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)))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	0.0b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.1b	(/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	4.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Compiler

Compiled 220 to 125 computations (43.2% saved)

series4.0ms (0%)

Counts

1 → 1

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite112.0ms (0.5%)

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	243	11
2	2659	11

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

simplify7.0ms (0%)

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

localize24.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	5.9b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
	0.1b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(sqrt.f64 (+.f64 1 y))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))
✓	0.1b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
✓	5.9b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))

Compiler

Compiled 54 to 33 computations (38.9% saved)

series38.0ms (0.2%)

Counts

3 → 14

Calls

18 calls:

Time	Variable		Point	Expression
29.0ms	y	@	-inf	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
1.0ms	x	@	-inf	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
1.0ms	x	@	inf	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
1.0ms	y	@	inf	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
1.0ms	x	@	0	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))

rewrite132.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`log-prod_binary64`
623×	`fma-neg_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
221×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	301	46
2	4680	46

Stop Event

1×	node limit

Counts

3 → 170

Calls

Call 1

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

Outputs

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

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

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
615×	`fma-neg_binary64`
486×	`unswap-sqr_binary64`
414×	`cancel-sign-sub-inv_binary64`
376×	`associate-+l+_binary64`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	45	200
1	122	194
2	314	194
3	974	182
4	2379	182
5	3275	182
6	4515	182
7	5717	181

Stop Event

1×	node limit

Counts

184 → 192

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

localize72.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	9.3b	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z)))
	0.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	0.1b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(sqrt.f64 (+.f64 1 z))
✓	0.1b	(+.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
✓	0.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	9.3b	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z)))

Compiler

Compiled 74 to 46 computations (37.8% saved)

series7.0ms (0%)

Counts

3 → 9

Calls

15 calls:

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

rewrite129.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

698×	`fma-neg_binary64`
288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
241×	`log-pow_binary64`
218×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	332	62
2	5095	62

Stop Event

1×	node limit

Counts

3 → 177

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	107
1	41	107
2	72	107
3	132	107
4	222	107
5	371	107
6	689	107
7	979	107
8	1378	107
9	1706	107
10	1958	107
11	1978	107

Stop Event

1×

saturated

Counts

186 → 188

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

localize83.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) -1) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	0.0b	(+.f64 (+.f64 (sqrt.f64 z) -1) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(sqrt.f64 (+.f64 1 y))
✓	0.0b	(+.f64 (+.f64 (sqrt.f64 z) -1) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))
✓	0.0b	(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) -1) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	4.4b	(-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))
✓	4.6b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) -1) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t)))))

Compiler

Compiled 144 to 89 computations (38.2% saved)

series17.0ms (0.1%)

Counts

3 → 15

Calls

27 calls:

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

rewrite127.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`log1p-udef_binary64`
262×	`add-sqr-sqrt_binary64`
258×	`*-un-lft-identity_binary64`
258×	`pow1_binary64`
243×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	96
1	498	96
2	7856	96

Stop Event

1×	node limit

Counts

3 → 141

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

844×	`sub-neg_binary64`
703×	`fma-neg_binary64`
506×	`distribute-neg-in_binary64`
424×	`associate-+l-_binary64`
407×	`associate--l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	325
1	155	325
2	424	325
3	1227	325
4	2726	325
5	4602	325
6	6988	325

Stop Event

1×	node limit

Counts

156 → 170

Calls

Call 1

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

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

localize84.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))
	0.0b	(sqrt.f64 (+.f64 1 y))
✓	0.0b	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t))
✓	0.1b	(-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))
	4.4b	(-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))
✓	56.0b	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))

Compiler

Compiled 136 to 83 computations (39% saved)

series47.0ms (0.2%)

Counts

3 → 14

Calls

27 calls:

Time	Variable		Point	Expression
30.0ms	z	@	inf	(+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t))
2.0ms	t	@	-inf	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))
2.0ms	t	@	inf	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))
1.0ms	t	@	0	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))
1.0ms	z	@	0	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))

rewrite105.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

425×	`log1p-udef_binary64`
257×	`add-sqr-sqrt_binary64`
253×	`pow1_binary64`
252×	`*-un-lft-identity_binary64`
241×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	98
1	497	90
2	7446	90

Stop Event

1×	node limit

Counts

3 → 111

Calls

Call 1

Inputs

(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))

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

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

Outputs

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

simplify49.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

865×	`sub-neg_binary64`
639×	`fma-def_binary64`
487×	`fma-neg_binary64`
430×	`associate-+l+_binary64`
426×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	280
1	124	280
2	332	280
3	988	280
4	3018	280
5	4562	280
6	7147	280

Stop Event

1×	node limit

Counts

125 → 137

Calls

Call 1

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

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

eval975.0ms (4.7%)

Compiler: Compiled 32501 to 20909 computations (35.7% saved)

prune390.0ms (1.9%)

Pruning

47 alts after pruning (44 fresh and 3 done)

	Pruned	Kept	Total
New	933	35	968
Fresh	9	9	18
Picked	0	1	1
Done	4	2	6
Total	946	47	993

Error

0.6b

Counts

993 → 47

Alt Table

Click to see full alt table

Status	Error	Program
✓	2.8b	(+.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)))
	35.5b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
▶	38.7b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
	42.6b	(+.f64 1 (+.f64 (exp.f64 (*.f64 1/2 (log1p.f64 z))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	35.5b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 x) (sqrt.f64 y))))
	42.4b	(+.f64 1 (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z)))))
	42.3b	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z)))
	4.8b	(+.f64 (+.f64 (+.f64 1 (/.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)))
	4.2b	(+.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)))
	42.3b	(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
	59.1b	(-.f64 (-.f64 (/.f64 (+.f64 1 y) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (/.f64 (+.f64 1 x) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
✓	56.4b	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (+.f64 (sqrt.f64 z) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))) (sqrt.f64 t)))))
	41.2b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 2 (sqrt.f64 x)))
	47.5b	(+.f64 1 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	42.7b	(+.f64 1 (+.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 z 1)))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	45.0b	(+.f64 1 (*.f64 (+.f64 1 (-.f64 z (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 2))) (/.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 z)))))
	42.3b	(expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 1))))
	2.9b	(+.f64 (+.f64 (+.f64 (.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)))) (-.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)))
	56.4b	(pow.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 t) 1)) (sqrt.f64 (+.f64 1 t)))) 2)
	42.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 1))) 2)
	35.5b	(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 1 (sqrt.f64 y)))
	42.5b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 1))) 3)
	59.7b	(fma.f64 (-.f64 y x) (/.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	3.8b	(+.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)))
	56.8b	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))
	59.1b	(-.f64 (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
▶	5.4b	(-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))
	42.3b	(+.f64 1 (fma.f64 (cbrt.f64 (+.f64 1 z)) (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z)))))
	24.9b	(+.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))))) 3))
	37.0b	(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	39.0b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
	35.7b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 2)
	56.5b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (+.f64 2 (sqrt.f64 (+.f64 1 t))))
	36.2b	(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	46.6b	(+.f64 1 (/.f64 (-.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 2) (+.f64 1 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) (sqrt.f64 (+.f64 1 z)))))
	56.5b	(*.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) -2)))))
	56.2b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (+.f64 1 (*.f64 1/2 z))) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	56.5b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 -1 (sqrt.f64 t))))
▶	0.9b	(+.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 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
✓	1.3b	(+.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)))
	4.4b	(+.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))))
	35.4b	(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 1 (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
▶	39.5b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	54.6b	(*.f64 1 (-.f64 (-.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 z))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))) (+.f64 (sqrt.f64 z) -1)))
	24.5b	(+.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	42.5b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 1)) 3))
▶	36.0b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)

Compiler

Compiled 2415 to 1910 computations (20.9% saved)

localize128.0ms (0.6%)

Local error

Found 8 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))))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(+.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 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
	0.1b	(/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	3.4b	(+.f64 z (-.f64 1 z))

Compiler

Compiled 253 to 146 computations (42.3% saved)

series4.0ms (0%)

Counts

2 → 13

Calls

6 calls:

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

rewrite93.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`fma-def_binary64`
545×	`log-prod_binary64`
347×	`fma-neg_binary64`
300×	`pow2_binary64`
206×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	236	18
2	3597	18

Stop Event

1×	node limit

Counts

2 → 247

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	13
1	4	13

Stop Event

1×

saturated

Counts

260 → 248

Calls

Call 1

Inputs
1
1
1
1
1
1
1
1
1
1
1
1
1

Outputs
1
1
1
1
1
1
1
1
1
1
1
1
1

localize10.0ms (0%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 22 to 15 computations (31.8% saved)

rewrite0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

localize28.0ms (0.1%)

Local error

Found 8 expressions with local error:

New	Error	Program
	4.4b	(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
	0.1b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(sqrt.f64 (+.f64 1 z))
✓	0.1b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
✓	4.4b	(-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))
✓	9.5b	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z)))

Compiler

Compiled 62 to 40 computations (35.5% saved)

series6.0ms (0%)

Counts

3 → 7

Calls

12 calls:

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

rewrite104.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`fma-neg_binary64`
287×	`expm1-udef_binary64`
286×	`log1p-udef_binary64`
240×	`log-pow_binary64`
234×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	331	52
2	5131	52

Stop Event

1×	node limit

Counts

3 → 182

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

350×	`fma-def_binary64`
304×	`fma-neg_binary64`
142×	`distribute-rgt-in_binary64`
129×	`associate--r+_binary64`
114×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	59
1	39	59
2	70	59
3	129	59
4	217	59
5	350	59
6	638	59
7	1108	59
8	1520	59
9	1820	59
10	2080	59
11	2108	59

Stop Event

1×

saturated

Counts

189 → 191

Calls

Call 1

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

Outputs
2
1
1
(-.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 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 (+.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)))

localize49.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)
	0.1b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
	0.0b	(-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.1b	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
✓	0.1b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)
✓	0.7b	(cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
✓	5.9b	(+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))

Compiler

Compiled 90 to 51 computations (43.3% saved)

series62.0ms (0.3%)

Counts

3 → 12

Calls

18 calls:

Time	Variable		Point	Expression
12.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)
8.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)
6.0ms	y	@	0	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)
6.0ms	y	@	inf	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)
5.0ms	x	@	inf	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 3)

rewrite103.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

623×	`fma-neg_binary64`
287×	`expm1-udef_binary64`
287×	`log1p-udef_binary64`
246×	`log-pow_binary64`
182×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	74
1	368	74
2	5051	74

Stop Event

1×	node limit

Counts

3 → 181

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

983×	`sqr-pow_binary64`
616×	`associate-l_binary64`
512×	`pow-sqr_binary64`
496×	`cube-prod_binary64`
432×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	158
1	66	158
2	119	158
3	224	158
4	441	158
5	916	158
6	2632	158
7	3061	158
8	3435	158
9	3879	158
10	4391	158
11	5155	158
12	5701	158
13	6278	158
14	6665	158
15	6923	158
16	7144	158

Stop Event

1×	node limit

Counts

193 → 125

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

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

localize86.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))
	0.0b	(sqrt.f64 (+.f64 1 z))
	0.0b	(sqrt.f64 (+.f64 1 y))
	0.0b	(-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))
✓	0.1b	(+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))))
✓	1.8b	(-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))
	4.4b	(-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y)))
✓	4.7b	(-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))

Compiler

Compiled 113 to 71 computations (37.2% saved)

series6.0ms (0%)

Counts

3 → 6

Calls

12 calls:

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

rewrite120.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

390×	`expm1-udef_binary64`
390×	`log1p-udef_binary64`
237×	`add-sqr-sqrt_binary64`
234×	`*-un-lft-identity_binary64`
234×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	49
1	449	49
2	6938	49

Stop Event

1×	node limit

Counts

3 → 113

Calls

Call 1

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

Outputs

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

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

352×	`fma-def_binary64`
304×	`fma-neg_binary64`
142×	`distribute-rgt-in_binary64`
129×	`associate--r+_binary64`
114×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	58
1	40	58
2	70	58
3	129	58
4	217	58
5	350	58
6	637	58
7	1105	58
8	1523	58
9	1823	58
10	2083	58
11	2111	58

Stop Event

1×

saturated

Counts

119 → 123

Calls

Call 1

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

eval1.1s (5.1%)

Compiler: Compiled 34268 to 21673 computations (36.8% saved)

prune311.0ms (1.5%)

Pruning

54 alts after pruning (50 fresh and 4 done)

	Pruned	Kept	Total
New	899	24	923
Fresh	13	26	39
Picked	0	1	1
Done	4	3	7
Total	916	54	970

Error

0.0b

Counts

970 → 54

Alt Table

Click to see full alt table

Status	Error	Program
	39.5b	(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
	35.5b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
✓	38.7b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
	42.6b	(+.f64 1 (+.f64 (exp.f64 (*.f64 1/2 (log1p.f64 z))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	40.2b	1
	35.5b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 x) (sqrt.f64 y))))
	41.9b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 1 (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) 2)
	4.8b	(+.f64 (+.f64 (+.f64 1 (/.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)))
	36.0b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 x) (sqrt.f64 y)))))) 3)
	42.0b	(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 1 (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) 3)
	42.3b	(-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z))
	41.2b	(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 2 (sqrt.f64 x)))
	42.7b	(+.f64 1 (+.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 z 1)))) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	22.9b	(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	42.0b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (pow.f64 (+.f64 1 z) 1/4) (pow.f64 (+.f64 1 z) 1/4) (-.f64 1 (sqrt.f64 z))))
	42.3b	(expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 1))))
	2.9b	(+.f64 (+.f64 (+.f64 (.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)))) (-.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)))
	37.7b	(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	56.4b	(pow.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 t) 1)) (sqrt.f64 (+.f64 1 t)))) 2)
	4.6b	(-.f64 (+.f64 1 (-.f64 (/.f64 (+.f64 1 (-.f64 z z)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))
	0.4b	(+.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 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	59.1b	(-.f64 (/.f64 (-.f64 y x) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
	47.4b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 1 (-.f64 1 (sqrt.f64 z))))
	59.7b	(fma.f64 (-.f64 y x) (/.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x)))) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	0.6b	(+.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 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (/.f64 (+.f64 1 (-.f64 t t)) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	3.8b	(+.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)))
	56.8b	(fma.f64 (pow.f64 (+.f64 1 t) 1/4) (pow.f64 (+.f64 1 t) 1/4) (+.f64 1 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))))
✓	5.4b	(-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))
	45.0b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (+.f64 (+.f64 1 (*.f64 1/2 z)) (-.f64 1 (sqrt.f64 z))))
	24.9b	(+.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))))) 3))
	39.0b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 (+.f64 1 x))) (log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))))
	38.5b	(-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))
	35.7b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))) 2)
	56.5b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (+.f64 2 (sqrt.f64 (+.f64 1 t))))
	56.2b	(+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (-.f64 (+.f64 1 (+.f64 1 (*.f64 1/2 z))) (sqrt.f64 z)) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))))
	37.8b	(+.f64 (/.f64 (+.f64 1 (-.f64 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
	36.2b	(fma.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 (+.f64 1 y) 1/4) (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
	41.9b	(exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 1 (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))))
	56.5b	(*.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 t) -2)))))
	36.1b	(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y))) 3)
	38.8b	(+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 1 (+.f64 y (+.f64 y (sqrt.f64 (*.f64 (+.f64 1 y) y)))))) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 1 (sqrt.f64 z))))
	42.3b	(+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z)))
	35.6b	(pow.f64 (pow.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 y))) (sqrt.f64 y)) 1/3) 3)
✓	1.3b	(+.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)))
	4.4b	(+.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))))
	53.1b	(+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (/.f64 (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 z)) 2) (+.f64 1 z)) (-.f64 (-.f64 1 (sqrt.f64 z)) (sqrt.f64 (+.f64 1 z)))))
	39.6b	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)
	19.4b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) (/.f64 (+.f64 z (-.f64 1 z)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	35.4b	(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 1 (sqrt.f64 (+.f64 1 y)))) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
✓	39.5b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	54.6b	(*.f64 1 (-.f64 (-.f64 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 (+.f64 1 z))) (+.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))) (sqrt.f64 t))) (+.f64 (sqrt.f64 z) -1)))
	24.5b	(+.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 z)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 z))))
	42.5b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 z))) 1)) 3))
	5.3b	(-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (/.f64 (-.f64 t (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))))

Compiler

Compiled 1389 to 1102 computations (20.7% saved)

regimes281.0ms (1.4%)

Counts

54 → 1

Calls

Call 1

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

Calls

15 calls:

48.0ms	t
33.0ms	z
32.0ms	y
29.0ms	x
11.0ms	(+.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
0.4b	1	`x`
0.4b	1	`y`
0.4b	1	`z`
0.4b	1	`t`
0.4b	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)))`
0.4b	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)))`
0.4b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
0.4b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
0.4b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1366 to 909 computations (33.5% saved)

regimes239.0ms (1.2%)

Counts

51 → 1

Calls

Call 1

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

14 calls:

31.0ms	t
28.0ms	y
28.0ms	x
26.0ms	z
13.0ms	(+.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	1	`x`
1.3b	1	`y`
1.3b	1	`z`
1.3b	1	`t`
1.3b	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)))`
1.3b	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)))`
1.3b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.3b	1	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
1.3b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.3b	1	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
1.3b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
1.3b	1	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
1.3b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
1.3b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1207 to 808 computations (33.1% saved)

regimes296.0ms (1.4%)

Counts

50 → 2

Calls

Call 1

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

Calls

14 calls:

46.0ms	y
44.0ms	x
24.0ms	z
24.0ms	t
21.0ms	(+.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
2.1b	2	`x`
2.1b	2	`y`
3.8b	1	`z`
3.8b	1	`t`
2.1b	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)))`
2.1b	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)))`
2.1b	2	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
2.1b	2	`(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))`
2.1b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
2.1b	2	`(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))`
2.1b	2	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
2.1b	2	`(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))`
3.8b	1	`(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))`
3.8b	1	`(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))`

Compiler

Compiled 1164 to 783 computations (32.7% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9999999999975556	1.0

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes151.0ms (0.7%)

Counts

44 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

41.0ms	y
39.0ms	x
22.0ms	t
22.0ms	z

Results

Error	Segments	Branch
2.9b	2	`x`
2.8b	2	`y`
5.3b	1	`z`
5.3b	1	`t`

Compiler

Compiled 805 to 531 computations (34% saved)

bsearch89.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
88.0ms	3.503589702041341e+22	1.297332130289082e+26

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes152.0ms (0.7%)

Counts

43 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

42.0ms	y
40.0ms	x
23.0ms	t
22.0ms	z

Results

Error	Segments	Branch
3.0b	2	`x`
2.9b	2	`y`
5.4b	1	`z`
5.4b	1	`t`

Compiler

Compiled 774 to 511 computations (34% saved)

bsearch94.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
93.0ms	3.503589702041341e+22	1.297332130289082e+26

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes329.0ms (1.6%)

Counts

39 → 2

Calls

Call 1

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

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

Calls

4 calls:

106.0ms	x
89.0ms	y
79.0ms	t
34.0ms	z

Results

Error	Segments	Branch
16.7b	6	`x`
13.4b	5	`y`
5.8b	2	`z`
14.3b	4	`t`

Compiler

Compiled 669 to 440 computations (34.2% saved)

bsearch110.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
109.0ms	15783650333863.982	18040468760131.64

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes342.0ms (1.7%)

Counts

16 → 4

Calls

Call 1

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

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

Calls

4 calls:

145.0ms	x
119.0ms	t
39.0ms	y
32.0ms	z

Results

Error	Segments	Branch
19.1b	4	`x`
15.9b	5	`y`
8.3b	4	`z`
16.0b	3	`t`

Compiler

Compiled 203 to 142 computations (30% saved)

bsearch351.0ms (1.7%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
169.0ms	15783650333863.982	18040468760131.64
92.0ms	4.598252216543102e-102	4.9541236081853485e-101
89.0ms	9.0485970089933e-126	9.013024851281742e-123

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes353.0ms (1.7%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

4 calls:

138.0ms	x
134.0ms	z
55.0ms	y
19.0ms	t

Results

Error	Segments	Branch
19.1b	4	`x`
15.9b	5	`y`
9.5b	2	`z`
19.7b	2	`t`

Compiler

Compiled 186 to 130 computations (30.1% saved)

bsearch90.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
90.0ms	15783650333863.982	18040468760131.64

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes72.0ms (0.3%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

4 calls:

31.0ms	t
17.0ms	y
13.0ms	x
9.0ms	z

Results

Error	Segments	Branch
21.5b	3	`x`
18.5b	4	`y`
9.5b	2	`z`
19.7b	2	`t`

Compiler

Compiled 59 to 46 computations (22% saved)

bsearch91.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
91.0ms	15783650333863.982	18040468760131.64

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes32.0ms (0.2%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

10.0ms	t
7.0ms	z
7.0ms	y
6.0ms	x

Results

Error	Segments	Branch
34.8b	2	`x`
26.3b	2	`y`
23.9b	2	`z`
33.6b	2	`t`

Compiler

Compiled 41 to 33 computations (19.5% saved)

bsearch183.0ms (0.9%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
183.0ms	1.1540684488253324e+31	2.0524112094426872e+33

Compiler

Compiled 42 to 33 computations (21.4% saved)

regimes15.0ms (0.1%)

Accuracy

Total -0.7b remaining (-1.8%)

Threshold costs -0.7b (-1.8%)

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:

4.0ms	x
3.0ms	y
3.0ms	z
3.0ms	t

Results

Error	Segments	Branch
39.5b	1	`x`
39.5b	1	`y`
39.5b	1	`z`
39.5b	1	`t`

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

69×	`+-commutative_binary64`
40×	`sub-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
24×	`distribute-neg-in_binary64`
22×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	623
1	165	623
2	225	623
3	280	623
4	340	623
5	368	623
6	381	623
7	390	623
8	404	623
9	412	623

Stop Event

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 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 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))) 1) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (-.f64 (/.f64 (+.f64 1 (-.f64 z z)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))))
(if (<=.f64 y 35035897020413407920128) (-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (/.f64 (-.f64 t (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 y 35035897020413407920128) (-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 3448174389064753/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (if (<=.f64 z 5797771594522111/1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (+.f64 2 (sqrt.f64 (+.f64 1 t)))) (if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))))
(if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 8081228970938359/512) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 11540684488253324235872522993664) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (-.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 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 y y)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 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 (+.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 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)) (+.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 (+.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)))
(if (<=.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 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (-.f64 (/.f64 (+.f64 1 (-.f64 z z)) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))))
(if (<=.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 1 (-.f64 (/.f64 (+.f64 1 (-.f64 z z)) (+.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z)))) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))))
(if (<=.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 1) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1 (-.f64 z z)) (+.f64 (sqrt.f64 z) (sqrt.f64 (+.f64 1 z)))) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
(if (<=.f64 y 35035897020413407920128) (-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (/.f64 (-.f64 t (+.f64 1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 y 35035897020413407920128) (-.f64 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (/.f64 (+.f64 t (-.f64 -1 t)) (+.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 y 35035897020413407920128) (+.f64 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (/.f64 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t))))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 y 35035897020413407920128) (-.f64 (+.f64 1 (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 y) (sqrt.f64 (+.f64 1 y))))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 y 35035897020413407920128) (+.f64 (+.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (-.f64 (sqrt.f64 t) (sqrt.f64 (+.f64 1 t)))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 8081228970938359/512) (+.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 3448174389064753/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (if (<=.f64 z 5797771594522111/1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (+.f64 2 (sqrt.f64 (+.f64 1 t)))) (if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))))
(if (<=.f64 z 3448174389064753/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (if (<=.f64 z 5797771594522111/1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300505812095689818112) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (+.f64 (sqrt.f64 z) (sqrt.f64 t))) (+.f64 (sqrt.f64 (+.f64 1 t)) 2)) (if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) 2) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))))
(if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 2 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 8081228970938359/512) (-.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) 2) (sqrt.f64 z)) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 8081228970938359/512) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
(if (<=.f64 z 11540684488253324235872522993664) (+.f64 (sqrt.f64 (+.f64 1 z)) (-.f64 2 (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
1

end451.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 946 to 678 computations (28.3% saved)

Iter	Nodes	Cost
0	97	623
1	165	623
2	225	623
3	280	623
4	340	623
5	368	623
6	381	623
7	390	623
8	404	623
9	412	623

Iter	Nodes	Cost
0	97	623
1	165	623
2	225	623
3	280	623
4	340	623
5	368	623
6	381	623
7	390	623
8	404	623
9	412	623

Iter	Nodes	Cost
0	97	623
1	165	623
2	225	623
3	280	623
4	340	623
5	368	623
6	381	623
7	390	623
8	404	623
9	412	623