Details

analyze390.0ms (3.1%)

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)

sample6.5s (51.8%)

Symmetry

(sort x y z t)

Results

2.4s	4469×	body	512	valid
2.0s	10124×	body	128	invalid
1.4s	1754×	body	1024	valid
408.0ms	1123×	body	256	valid
194.0ms	910×	body	128	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify47.0ms (0.4%)

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

4.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.2b	(+.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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.1b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	6.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series43.0ms (0.3%)

Counts

4 → 4

Calls

4 calls:

12.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
11.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
10.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite65.0ms (0.5%)

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

simplify273.0ms (2.2%)

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

prune584.0ms (4.7%)

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

0.4b

Counts

254 → 5

Alt Table

Status	Error	Program
	4.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.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)))
	3.6b	(+.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)))
	3.3b	(+.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)))
▶	2.3b	(+.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)))
	3.6b	(+.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))))

Compiler

Compiled 12243 to 6886 computations (43.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	2.1b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	6.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series10.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

10.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

1 → 47

Calls

1 calls:

7.0ms

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

simplify174.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub_binary64`
502×	`associate-+l+_binary64`
423×	`associate-+r+_binary64`
330×	`associate-+l-_binary64`
310×	`times-frac_binary64`

Counts

48 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	845
1	100	785
2	197	785
3	383	785
4	949	785
5	2306	785
6	4846	785
7	5785	785

prune546.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	234	6	240

Error

0.1b

Counts

240 → 6

Alt Table

Status	Error	Program
▶	1.4b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (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)))
	4.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.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)))
	3.6b	(+.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)))
	3.6b	(+.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))))
	1.5b	(+.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)))
	2.3b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.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)))

Compiler

Compiled 11620 to 6938 computations (40.3% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.3b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
	2.1b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series9.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

9.0ms

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

1 → 47

Calls

1 calls:

9.0ms

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

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub_binary64`
502×	`associate-+l+_binary64`
423×	`associate-+r+_binary64`
330×	`associate-+l-_binary64`
310×	`times-frac_binary64`

Counts

48 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	845
1	100	785
2	197	785
3	383	785
4	949	785
5	2306	785
6	4846	785
7	5785	785

prune464.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	217	5	222

Error

0.0b

Counts

222 → 5

Alt Table

Status	Error	Program
	4.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.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)))
	3.6b	(+.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)))
	2.3b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.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)))
▶	0.7b	(+.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 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	0.8b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))

Compiler

Compiled 10728 to 6768 computations (36.9% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	0.3b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
	3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series10.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

10.0ms

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

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

1 → 47

Calls

1 calls:

8.0ms

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

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub_binary64`
502×	`associate-+l+_binary64`
423×	`associate-+r+_binary64`
330×	`associate-+l-_binary64`
310×	`times-frac_binary64`

Counts

48 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	845
1	100	785
2	197	785
3	383	785
4	949	785
5	2306	785
6	4846	785
7	5785	785

prune359.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	199	4	203

Error

0.0b

Counts

203 → 4

Alt Table

Status	Error	Program
	2.8b	(+.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 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	0.1b	(+.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 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	0.7b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.2b	(+.f64 (+.f64 (+.f64 (expm1.f64 (log1p.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 9623 to 6411 computations (33.4% saved)

regimes2.6s (20.5%)

Accuracy

Total 0.0b remaining (41.6%)

Threshold costs 0.0b (41.6%)

Counts

152 → 1

Compiler

Compiled 109653 to 78524 computations (28.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	62
1	42	62
2	41	62

end181.0ms (1.4%)

Remove: (sort x y z t)
Compiler: Compiled 344 to 277 computations (19.5% saved)

Details

analyze390.0ms (3.1%)

sample6.5s (51.8%)

simplify47.0ms (0.4%)

prune3.0ms (0%)

localize20.0ms (0.2%)

series43.0ms (0.3%)

rewrite65.0ms (0.5%)

simplify273.0ms (2.2%)

prune584.0ms (4.7%)

localize20.0ms (0.2%)

series10.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify174.0ms (1.4%)

prune546.0ms (4.4%)

localize29.0ms (0.2%)

series9.0ms (0.1%)

rewrite13.0ms (0.1%)

simplify93.0ms (0.7%)

prune464.0ms (3.7%)

localize32.0ms (0.3%)

series10.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify96.0ms (0.8%)

prune359.0ms (2.9%)

regimes2.6s (20.5%)

simplify3.0ms (0%)

end181.0ms (1.4%)

Profiling