Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.1s (39.4%)

Results

1.0s	2167×	body	2048	valid
468.0ms	4300×	body	128	valid
377.0ms	1009×	body	1024	valid
148.0ms	507×	body	512	valid
50.0ms	273×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	35	15
4	42	15
5	52	15
6	60	15
7	69	15
8	72	15
9	53	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	2.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series17.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 117

Calls

4 calls:

7.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
471×	`associate-l_binary64`
406×	`associate-r_binary64`
399×	`fma-neg_binary64`
286×	`cancel-sign-sub-inv_binary64`

Counts

165 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3449
1	643	3086
2	1771	2766
3	4772	2766
4	4875	2766

prune162.0ms (3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	2	202

Error

0.0b

Counts

202 → 2

Alt Table

Status	Error	Program
	31.5b	(*.f64 1/8 (pow.f64 x 2))
▶	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 4480 to 3991 computations (10.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	1.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series9.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

2 → 90

Calls

2 calls:

6.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

767×	`times-frac_binary64`
691×	`fma-def_binary64`
261×	`associate-/l*_binary64`
242×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`

Counts

114 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	2633
1	725	1921
2	1892	1557
3	4522	1557
4	5585	1557

prune262.0ms (4.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	221	4	225

Error

0.0b

Counts

225 → 4

Alt Table

Status	Error	Program
	31.5b	(*.f64 1/8 (pow.f64 x 2))
	14.5b	(/.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (neg.f64 (.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x))) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))
▶	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

Compiler

Compiled 7445 to 6604 computations (11.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	1.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
5.0ms	(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`log-pow_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`exp-prod_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

9.0ms	(+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
5.0ms	(log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

351×	`fma-neg_binary64`
320×	`sub-neg_binary64`
240×	`fma-def_binary64`
207×	`associate-*l/_binary64`
196×	`neg-mul-1_binary64`

Counts

66 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1304
1	328	1210
2	833	1182
3	2569	1174
4	4860	1165
5	4979	1165

prune297.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	247	4	251

Error

Counts

251 → 4

Alt Table

Status	Error	Program
	14.5b	(/.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (neg.f64 (.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x))) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)))) (+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
▶	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))
	31.5b	(*.f64 1/8 (pow.f64 x 2))
✓	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

Compiler

Compiled 8589 to 7676 computations (10.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
	1.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series61.0ms (1.1%)

Counts

3 → 16

Calls

3 calls:

23.0ms	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
21.0ms	(+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
14.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`sqrt-prod_binary64`
11×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 54

Calls

3 calls:

2.0ms	(+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
2.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-neg_binary64`
379×	`sub-neg_binary64`
279×	`fma-def_binary64`
200×	`associate-/l*_binary64`
194×	`distribute-neg-frac_binary64`

Counts

70 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	1528
1	345	1439
2	932	1425
3	3452	1423
4	4933	1423
5	4940	1423

prune250.0ms (4.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	187	4	191

Error

Counts

191 → 4

Alt Table

Status	Error	Program
	31.5b	(*.f64 1/8 (pow.f64 x 2))
	14.5b	(/.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (neg.f64 (.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x))) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (.f64 (/.f64 (cbrt.f64 1/2) (hypot.f64 1 x)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)))) (+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))
✓	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))
✓	14.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

Compiler

Compiled 6842 to 6132 computations (10.4% saved)

regimes1.5s (28%)

Accuracy

Total 0.0b remaining (2.9%)

Threshold costs 0.0b (2.9%)

Counts

161 → 3

Compiler

Compiled 31306 to 28378 computations (9.4% saved)

bsearch49.0ms (0.9%)

Steps

Iters	Range		Point
10	1.3491531036351671e-12	1.3717918192523137	0.00012153717904520032
9	-0.20611028169239645	-1.1233212943995242e-9	-0.00010956238046010226

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	100
1	45	100
2	55	100
3	59	100
4	61	100
5	58	100

end138.0ms (2.6%)

Compiler: Compiled 247 to 220 computations (10.9% saved)

Details

analyze1.0ms (0%)

sample2.1s (39.4%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series17.0ms (0.3%)

rewrite24.0ms (0.4%)

simplify116.0ms (2.2%)

prune162.0ms (3%)

localize8.0ms (0.1%)

series9.0ms (0.2%)

rewrite18.0ms (0.3%)

simplify96.0ms (1.8%)

prune262.0ms (4.9%)

localize11.0ms (0.2%)

series10.0ms (0.2%)

rewrite15.0ms (0.3%)

simplify80.0ms (1.5%)

prune297.0ms (5.6%)

localize9.0ms (0.2%)

series61.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify83.0ms (1.6%)

prune250.0ms (4.7%)

regimes1.5s (28%)

bsearch49.0ms (0.9%)

simplify9.0ms (0.2%)

end138.0ms (2.6%)

Profiling