Details

analyze514.0ms (4.9%)

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
2%	13.3%	84.8%	13
2.3%	11.4%	86.3%	14

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample6.7s (64%)

Results

2.7s	4516×	body	512	valid
2.0s	9755×	body	128	invalid
1.4s	1771×	body	1024	valid
448.0ms	1051×	body	256	valid
194.0ms	917×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 72 to 56 computations (22.2% saved)

preprocess48.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

770×	`sub-neg_binary64`
524×	`fma-neg_binary64`
396×	`associate-+l+_binary64`
382×	`fma-def_binary64`
378×	`distribute-neg-in_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
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 (+.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 (+.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 (+.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 (+.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 (+.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 (+.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))))))

Symmetry

(sort x y z t)

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

531×	`associate-+r-_binary64`
502×	`associate-+l-_binary64`
451×	`associate--r+_binary64`
355×	`associate--r-_binary64`
345×	`+-commutative_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))))))

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

5.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.7b	(+.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))))))
▶	5.8b	(+.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)))

Status

Error

Program

6.7b

(+.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))))))

▶

5.8b

(+.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)))

Compiler

Compiled 206 to 154 computations (25.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.5b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
✓	3.8b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series14.0ms (0.1%)

Counts

4 → 4

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.0ms	y	@	inf	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
1.0ms	z	@	inf	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
1.0ms	y	@	0	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
1.0ms	t	@	inf	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`add-sqr-sqrt_binary64`
261×	`*-un-lft-identity_binary64`
261×	`pow1_binary64`
243×	`add-cbrt-cube_binary64`
243×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	504	44

Stop Event

1×	node limit

Counts

4 → 96

Calls

Call 1

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

Outputs
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simplify7.0ms (0.1%)

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

100 → 97

Calls

Call 1

Inputs
1
1
1
1

Outputs
1
1
1
1

prune250.0ms (2.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	83	14	97
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	14	99

Error

4.2b

Counts

99 → 14

Alt Table

Status	Error	Program
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	5.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.4b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 1 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)))
	40.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	20.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 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)))
	19.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (cbrt.f64 (sqrt.f64 (+.f64 y 1)))) (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.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))) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
	5.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	5.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.f64 (-.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)))
	40.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (cbrt.f64 (sqrt.f64 (+.f64 1 z)))) (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 1 (sqrt.f64 (+.f64 1 x)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (.f64 (cbrt.f64 (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (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)))

Compiler

Compiled 5545 to 3368 computations (39.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.4b	(-.f64 (+.f64 y 1) y)
	2.5b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

669×	`pow1_binary64`
628×	`log1p-expm1-u_binary64`
628×	`expm1-log1p-u_binary64`
627×	`add-log-exp_binary64`
61×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	7
2	1674	7

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

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

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

Outputs

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12

Stop Event

1×

saturated

Counts

58 → 47

Calls

Call 1

Inputs
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

prune466.0ms (4.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	118	15	133

Error

3.9b

Counts

133 → 15

Alt Table

Status	Error	Program
	5.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (log.f64 (+.f64 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	5.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	40.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	20.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 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)))
	19.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (cbrt.f64 (sqrt.f64 (+.f64 y 1)))) (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
	40.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (cbrt.f64 (sqrt.f64 (+.f64 1 z)))) (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 1 (sqrt.f64 (+.f64 1 x)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (.f64 (cbrt.f64 (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (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)))
▶	4.8b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (-.f64 (+.f64 y 1) y) (+.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)))

Compiler

Compiled 7083 to 4429 computations (37.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (+.f64 1 x) x)
	2.4b	(-.f64 (+.f64 y 1) y)
	2.5b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite28.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`pow1_binary64`
537×	`log1p-expm1-u_binary64`
537×	`expm1-log1p-u_binary64`
536×	`add-log-exp_binary64`
60×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	114	1
2	1722	1

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x . 1)))))

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12

Stop Event

1×

saturated

Counts

13 → 1

Calls

Call 1

Inputs
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

prune339.0ms (3.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	97	14	111

Error

1.3b

Counts

111 → 14

Alt Table

Status	Error	Program
	5.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (log.f64 (+.f64 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (-.f64 (+.f64 y 1) y) (+.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)))
	4.4b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	5.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	2.1b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))
	40.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	20.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (-.f64 (+.f64 y 1) y) (+.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)))
	40.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (cbrt.f64 (sqrt.f64 (+.f64 1 z)))) (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.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)))
	19.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (cbrt.f64 (sqrt.f64 (+.f64 y 1)))) (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 6348 to 4059 computations (36.1% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
	2.4b	(-.f64 (+.f64 y 1) y)
	2.5b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series3.0ms (0%)

Counts

1 → 1

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

615×	`fma-def_binary64`
322×	`fma-neg_binary64`
181×	`log1p-udef_binary64`
180×	`expm1-udef_binary64`
156×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	212	11
2	3311	11

Stop Event

1×	node limit

Counts

1 → 156

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 y 1)) (neg.f64 (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 y 1)) (*.f64 -1 (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 y 1)) (*.f64 (neg.f64 (cbrt.f64 y)) (cbrt.f64 (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 y 1)) (*.f64 (neg.f64 (pow.f64 y 1/4)) (pow.f64 y 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (fma.f64 (neg.f64 (sqrt.f64 y)) 1 (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 y))) (cbrt.f64 y) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (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 (/.f64 (+.f64 y 1) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (neg.f64 (/.f64 y (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 y 1) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 y (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (-.f64 y y)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (-.f64 y y))) 2) (*.f64 (cbrt.f64 (+.f64 1 (-.f64 y y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (-.f64 y y))) (*.f64 (sqrt.f64 (+.f64 1 (-.f64 y y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 1 (-.f64 y y))) (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 1 (-.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 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simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

Counts

157 → 157

Calls

Call 1

Inputs
1

Outputs
1

prune832.0ms (7.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	253	13	266

Error

0.9b

Counts

266 → 13

Alt Table

Status	Error	Program
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (/.f64 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	5.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (-.f64 (+.f64 y 1) y) (+.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)))
	2.7b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (cbrt.f64 (sqrt.f64 (+.f64 1 z)))) (cbrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	1.5b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.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)))
	40.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	20.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.2b	(+.f64 (+.f64 (+.f64 (log.f64 (+.f64 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (-.f64 (+.f64 y 1) y) (+.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)))
	40.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (sqrt.f64 (sqrt.f64 (+.f64 1 z))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.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)))
	18.8b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (cbrt.f64 (+.f64 y 1)) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.1b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))))

Compiler

Compiled 12901 to 8212 computations (36.3% saved)

regimes661.0ms (6.3%)

Accuracy

Total 0.5b remaining (43.7%)

Threshold costs 0.5b (43.7%)

Counts

135 → 1

Compiler

Compiled 5891 to 3728 computations (36.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	56
1	42	56
2	49	56
3	53	56
4	55	56

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

end332.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 756 to 553 computations (26.9% saved)

Details

analyze514.0ms (4.9%)

sample6.7s (64%)

preprocess48.0ms (0.5%)

simplify28.0ms (0.3%)

prune6.0ms (0.1%)

localize20.0ms (0.2%)

series14.0ms (0.1%)

rewrite40.0ms (0.4%)

simplify7.0ms (0.1%)

prune250.0ms (2.4%)

localize27.0ms (0.3%)

series1.0ms (0%)

rewrite37.0ms (0.3%)

simplify8.0ms (0.1%)

prune466.0ms (4.4%)

localize29.0ms (0.3%)

series1.0ms (0%)

rewrite28.0ms (0.3%)

simplify6.0ms (0.1%)

prune339.0ms (3.2%)

localize28.0ms (0.3%)

series3.0ms (0%)

rewrite65.0ms (0.6%)

simplify10.0ms (0.1%)

prune832.0ms (7.9%)

regimes661.0ms (6.3%)

simplify3.0ms (0%)

end332.0ms (3.1%)

Profiling