Details

analyze2.0ms (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)

sample4.0s (40.6%)

Results

2.1s	2232×	body	2048	valid
803.0ms	4228×	body	128	valid
721.0ms	1069×	body	1024	valid
242.0ms	495×	body	512	valid
92.0ms	232×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify16.0ms (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

prune5.0ms (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

15.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(hypot.f64 1 x)
✓	1.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series31.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

12.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
8.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
6.0ms	(/.f64 1/2 (hypot.f64 1 x))
5.0ms	(hypot.f64 1 x)

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 110

Calls

4 calls:

16.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
13.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

simplify206.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
463×	`fma-neg_binary64`
398×	`times-frac_binary64`
372×	`associate-l_binary64`
332×	`associate-r_binary64`

Counts

158 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3244
1	653	2896
2	1804	2575
3	4560	2539
4	4860	2539
5	5266	2539

prune340.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
	28.9b	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
	15.7b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
▶	15.1b	(/.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))))))
	15.5b	(-.f64 1 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 4514 to 4011 computations (11.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 x)
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	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))))))
✓	0.6b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series63.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

44.0ms

(/.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))))))

12.0ms

(+.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)))

rewrite64.0ms (0.6%)

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:

25.0ms

(/.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))))))

11.0ms

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

7.0ms

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

simplify285.0ms (2.9%)

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

prune627.0ms (6.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	298	3	301

Error

Counts

301 → 3

Alt Table

Status	Error	Program
	15.5b	(exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
▶	15.1b	(/.f64 (log1p.f64 (expm1.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))))))
	28.9b	(-.f64 (fma.f64 (.f64 x x) 1/8 (.f64 (pow.f64 x 6) 69/1024)) (fma.f64 (pow.f64 x 4) 11/128 (*.f64 (pow.f64 x 8) 1843/32768)))

Compiler

Compiled 10602 to 9445 computations (10.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(expm1.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(/.f64 (log1p.f64 (expm1.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))))))
	0.6b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series54.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

46.0ms	(/.f64 (log1p.f64 (expm1.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))))))
8.0ms	(expm1.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
16×	`distribute-lft-out_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

16.0ms	(/.f64 (log1p.f64 (expm1.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))))))
1.0ms	(expm1.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

689×	`fma-def_binary64`
577×	`distribute-rgt-in_binary64`
411×	`times-frac_binary64`
218×	`fma-neg_binary64`
182×	`cancel-sign-sub-inv_binary64`

Counts

78 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3267
1	699	2938
2	2354	2877
3	4758	2874
4	5153	2874

prune522.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	263	3	266

Error

Counts

266 → 3

Alt Table

Status	Error	Program
▶	15.5b	(exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	15.1b	(/.f64 (log1p.f64 (expm1.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))))))
	28.9b	(-.f64 (fma.f64 (.f64 x x) 1/8 (.f64 (pow.f64 x 6) 69/1024)) (fma.f64 (pow.f64 x 4) 11/128 (*.f64 (pow.f64 x 8) 1843/32768)))

Compiler

Compiled 10174 to 9129 computations (10.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	0.1b	(exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	0.4b	(log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	0.6b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series124.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

62.0ms

(exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

36.0ms

(-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

25.0ms

(log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
24×	`prod-diff_binary64`
23×	`add-cube-cbrt_binary64`
22×	`exp-sum_binary64`

Counts

3 → 96

Calls

3 calls:

15.0ms

(exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

15.0ms

(-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

1.0ms

(log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify165.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

432×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
273×	`fma-def_binary64`
253×	`associate-+r+_binary64`
238×	`+-commutative_binary64`

Counts

132 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	6807
1	987	5723
2	3645	5105
3	4936	5105

prune494.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	276	3	279

Error

Counts

279 → 3

Alt Table

Status	Error	Program
✓	15.5b	(exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	15.1b	(/.f64 (log1p.f64 (expm1.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))))))
	28.9b	(-.f64 (fma.f64 (.f64 x x) 1/8 (.f64 (pow.f64 x 6) 69/1024)) (fma.f64 (pow.f64 x 4) 11/128 (*.f64 (pow.f64 x 8) 1843/32768)))

Compiler

Compiled 12547 to 11272 computations (10.2% saved)

regimes2.2s (22.6%)

Accuracy

Total 0.0b remaining (14.4%)

Threshold costs 0.0b (14.4%)

Counts

155 → 3

Compiler

Compiled 20629 to 18518 computations (10.2% saved)

bsearch86.0ms (0.9%)

Steps

Iters	Range		Point
9	0.00589096569095051	75899.98641191647	0.028761853505194473
10	-126.16804619797426	-5.750330009187192e-15	-0.027965099262194516

Compiler

Compiled 2 to 1 computations (50% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	104
1	58	104
2	68	104
3	92	104
4	102	104
5	108	104
6	110	104
7	106	104

end225.0ms (2.3%)

Compiler: Compiled 203 to 174 computations (14.3% saved)

Details

analyze2.0ms (0%)

sample4.0s (40.6%)

simplify16.0ms (0.2%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

series31.0ms (0.3%)

rewrite47.0ms (0.5%)

simplify206.0ms (2.1%)

prune340.0ms (3.4%)

localize18.0ms (0.2%)

series63.0ms (0.6%)

rewrite64.0ms (0.6%)

simplify285.0ms (2.9%)

prune627.0ms (6.4%)

localize20.0ms (0.2%)

series54.0ms (0.5%)

rewrite25.0ms (0.3%)

simplify117.0ms (1.2%)

prune522.0ms (5.3%)

localize20.0ms (0.2%)

series124.0ms (1.3%)

rewrite49.0ms (0.5%)

simplify165.0ms (1.7%)

prune494.0ms (5%)

regimes2.2s (22.6%)

bsearch86.0ms (0.9%)

simplify11.0ms (0.1%)

end225.0ms (2.3%)

Profiling