Details

analyze372.0ms (0.2%)

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
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample6.6s (4.4%)

Symmetry

(sort x y z t)

Results

2.6s	4590×	body	512	valid
2.0s	9890×	body	128	invalid
1.2s	1697×	body	1024	valid
439.0ms	1075×	body	256	valid
181.0ms	893×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify49.0ms (0%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
529×	`associate-+r-_binary64`
510×	`associate-+l-_binary64`
481×	`associate--r+_binary64`
355×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	54	50
2	166	50
3	893	50
4	4070	50
5	4939	50
6	5040	50

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

4.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.9b	(+.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 136 to 100 computations (26.5% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	3.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	5.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series68.0ms (0%)

Counts

4 → 4

Calls

4 calls:

19.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
17.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
17.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite56.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`sqrt-prod_binary64`
208×	`*-un-lft-identity_binary64`
168×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
124×	`add-cube-cbrt_binary64`

Counts

4 → 300

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
7.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
7.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
7.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify293.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

784×	`times-frac_binary64`
760×	`fma-neg_binary64`
360×	`exp-prod_binary64`
312×	`*-commutative_binary64`
308×	`fabs-mul_binary64`

Counts

304 → 253

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	9256
1	583	4524
2	1602	3684
3	3485	3684
4	4297	3684
5	4453	3684
6	4714	3684
7	4774	3684
8	5084	3684

prune455.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	248	5	253
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	5	254

Error

0.8b

Counts

254 → 5

Alt Table

Status	Error	Program
	4.6b	(+.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 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	4.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (.f64 (.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	3.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	3.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	2.8b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.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)))

Compiler

Compiled 12273 to 6904 computations (43.7% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (/.f64 1 (+.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)))
	2.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	5.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series51.0ms (0%)

Counts

1 → 7

Calls

1 calls:

51.0ms

(+.f64 (+.f64 (/.f64 1 (+.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)))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
49×	`associate-+r+_binary64`
48×	`sqrt-prod_binary64`
42×	`prod-diff_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

1 → 95

Calls

1 calls:

35.0ms

(+.f64 (+.f64 (/.f64 1 (+.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)))

simplify141.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

525×	`+-commutative_binary64`
300×	`distribute-rgt-in_binary64`
292×	`distribute-lft-in_binary64`
162×	`fma-neg_binary64`
159×	`associate-l_binary64`

Counts

102 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	5251
1	635	4984
2	2701	4873
3	4766	4873
4	4932	4873

prune640.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	298	5	303

Error

0.0b

Counts

303 → 5

Alt Table

Status	Error	Program
	4.6b	(+.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 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
▶	0.8b	(+.f64 (/.f64 (fma.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	2.9b	(+.f64 (/.f64 (+.f64 (.f64 (+.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) (pow.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) 3)) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (.f64 (+.f64 (.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (-.f64 (.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))))) (-.f64 (.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 (+.f64 z 1))) (.f64 (sqrt.f64 z) (sqrt.f64 z))))) (.f64 (+.f64 (.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (-.f64 (.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (/.f64 1 (+.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)))
	3.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	1.2b	(+.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 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 16603 to 9739 computations (41.3% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
✓	0.1b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))
✓	0.6b	(/.f64 (fma.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (.f64 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))
	2.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

Details

analyze372.0ms (0.2%)

sample6.6s (4.4%)

simplify49.0ms (0%)

prune3.0ms (0%)

localize21.0ms (0%)

series68.0ms (0%)

rewrite56.0ms (0%)

simplify293.0ms (0.2%)

prune455.0ms (0.3%)

localize25.0ms (0%)

series51.0ms (0%)

rewrite53.0ms (0%)

simplify141.0ms (0.1%)

prune640.0ms (0.4%)

localize29.0ms (0%)

series2.4min (94.1%)

Profiling