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 (54.5%)

Results

1.1s	2167×	body	2048	valid
459.0ms	4313×	body	128	valid
390.0ms	1046×	body	1024	valid
146.0ms	502×	body	512	valid
43.0ms	228×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify8.0ms (0.2%)

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

13.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.2b	(-.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	(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))))
✓	1.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series15.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(-.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	(hypot.f64 1 x)
2.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
22×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

4 → 98

Calls

4 calls:

8.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	(hypot.f64 1 x)

simplify119.0ms (3%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
495×	`associate-l_binary64`
429×	`fma-neg_binary64`
427×	`associate-r_binary64`
268×	`cancel-sign-sub-inv_binary64`

Counts

146 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	3114
1	607	2734
2	1733	2412
3	4850	2412
4	4972	2412

prune176.0ms (4.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Error

0.0b

Counts

182 → 3

Alt Table

Status	Error	Program
▶	12.7b	(/.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))))))
	32.1b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
	13.2b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 4140 to 3674 computations (11.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.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))))))
	0.0b	(sqrt.f64 (+.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)))))
✓	0.7b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series27.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

19.0ms

(/.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))))))

4.0ms

(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

3.0ms

(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

3 → 157

Calls

3 calls:

14.0ms

(/.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))))))

6.0ms

(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

6.0ms

(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify159.0ms (4%)

Algorithm

1×	egg-herbie

Rules

565×	`times-frac_binary64`
260×	`fma-def_binary64`
206×	`associate-r_binary64`
200×	`associate-/r*_binary64`
184×	`fma-neg_binary64`

Counts

193 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	8251
1	1249	5965
2	3887	5923
3	5050	5923

prune298.0ms (7.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	270	4	274

Error

Counts

274 → 4

Alt Table

Status	Error	Program
✓	12.7b	(/.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))))))
	32.1b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
	32.4b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
▶	13.2b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 10067 to 8998 computations (10.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.5b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	0.5b	(expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	1.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series16.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
5.0ms	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0ms	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-def_binary64`
447×	`associate-/r*_binary64`
447×	`fma-neg_binary64`
370×	`times-frac_binary64`
298×	`associate-l_binary64`

Counts

46 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1459
1	425	1327
2	1458	1228
3	4893	1228
4	5170	1228

prune169.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	181	4	185

Error

Counts

185 → 4

Alt Table

Status	Error	Program
✓	12.7b	(/.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))))))
▶	32.1b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
	32.4b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	13.2b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 4962 to 4465 computations (10% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6)))
✓	0.0b	(*.f64 69/1024 (pow.f64 x 6))
✓	18.5b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))

series15.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

7.0ms	(fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6)))
4.0ms	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
3.0ms	(*.f64 69/1024 (pow.f64 x 6))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(*.f64 69/1024 (pow.f64 x 6))
0.0ms	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
0.0ms	(fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6)))

simplify54.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

454×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
425×	`fma-def_binary64`
392×	`unswap-sqr_binary64`
362×	`associate-l_binary64`

Counts

71 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	1126
1	159	1024
2	366	992
3	1593	992
4	5137	992

prune55.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	73	4	77

Error

Counts

77 → 4

Alt Table

Status	Error	Program
✓	12.7b	(/.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))))))
✓	32.1b	(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
	32.4b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	13.2b	(log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 1554 to 1090 computations (29.9% saved)

regimes402.0ms (10.2%)

Accuracy

Total 0.0b remaining (58.8%)

Threshold costs 0.0b (58.8%)

Counts

49 → 2

Compiler

Compiled 5825 to 5209 computations (10.6% saved)

bsearch2.0ms (0%)

Compiler: Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	57
1	33	57
2	40	57
3	42	57
4	43	57
5	41	57

end101.0ms (2.6%)

Compiler: Compiled 139 to 115 computations (17.3% saved)

Details

analyze1.0ms (0%)

sample2.1s (54.5%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series15.0ms (0.4%)

rewrite22.0ms (0.6%)

simplify119.0ms (3%)

prune176.0ms (4.5%)

localize8.0ms (0.2%)

series27.0ms (0.7%)

rewrite44.0ms (1.1%)

simplify159.0ms (4%)

prune298.0ms (7.6%)

localize9.0ms (0.2%)

series16.0ms (0.4%)

rewrite1.0ms (0%)

simplify68.0ms (1.7%)

prune169.0ms (4.3%)

localize8.0ms (0.2%)

series15.0ms (0.4%)

rewrite6.0ms (0.2%)

simplify54.0ms (1.4%)

prune55.0ms (1.4%)

regimes402.0ms (10.2%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end101.0ms (2.6%)

Profiling