Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample823.0ms (26.9%)

Results

734.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify86.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

765×	`rules-24-rev_binary64`
397×	`rules-22-rev_binary64`
374×	`rules-23-rev_binary64`
342×	`cube-div_binary64`
250×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	15	4
2	36	4
3	107	4
4	297	4
5	1316	4
6	4411	4
7	4938	4

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(hypot.f64 x x)

rewrite38.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

280×	`log1p-expm1-u_binary64`
280×	`expm1-log1p-u_binary64`
260×	`add-cbrt-cube_binary64`
252×	`add-exp-log_binary64`
252×	`add-log-exp_binary64`

Counts

1 → 54

Calls

1 calls:

37.0ms

(hypot.f64 x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	70	4
2	844	4
3	5056	4
0	0	0
1	0	0

simplify44.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

791×	`rules-20_binary64`
783×	`fma-def_binary64`
400×	`fma-neg_binary64`
360×	`rules-14-rev_binary64`
313×	`rules-21_binary64`

Counts

66 → 56

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	72
1	13	72
2	19	72
3	25	72
4	37	72
5	47	72
6	90	72
7	312	72
8	1436	72
9	2550	72
10	11	72

prune26.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	6	57

Error

0.0b

Counts

57 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	40.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	1.4b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
	33.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.3b	(.f64 -1 (.f64 (sqrt.f64 2) x))

Compiler

Compiled 573 to 277 computations (51.7% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

series18.0ms (0.6%)

Counts

2 → 0

Calls

2 calls:

12.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
6.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite92.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

424×	`log1p-expm1-u_binary64`
424×	`expm1-log1p-u_binary64`
297×	`fma-neg_binary64`
286×	`unpow-prod-down_binary64`
199×	`log-prod_binary64`

Counts

2 → 169

Calls

2 calls:

88.0ms	(sqrt.f64 (hypot.f64 x x))
88.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	122	10
2	1292	10
3	4925	10
4	4961	10
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune108.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	223	8	231

Error

0.0b

Counts

231 → 8

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	40.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	33.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	31.6b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
▶	0.9b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
	1.4b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
	30.3b	(.f64 -1 (.f64 (sqrt.f64 2) x))

Compiler

Compiled 3520 to 1567 computations (55.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
✓	0.7b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)

series430.0ms (14.1%)

Counts

3 → 36

Calls

3 calls:

244.0ms	(pow.f64 (hypot.f64 x x) 1/4)
182.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)
4.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))

rewrite127.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
500×	`fma-neg_binary64`
289×	`fma-def_binary64`
209×	`egg-rr`

Counts

3 → 209

Calls

3 calls:

123.0ms	(pow.f64 (hypot.f64 x x) 1/4)
123.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
123.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	191	18
2	1816	18
3	4998	18
4	4924	18
5	5057	18
0	0	0
1	0	0

simplify45.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
683×	`fma-neg_binary64`
501×	`rules-13_binary64`
298×	`rules-20_binary64`
260×	`rules-15-rev_binary64`

Counts

245 → 222

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	504
1	66	500
2	124	428
3	342	348
4	1358	312
5	4907	312

prune208.0ms (6.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	367	4	371
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	370	9	379

Error

0.0b

Counts

379 → 9

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	40.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	33.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.6b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	0.9b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
	1.1b	(.f64 (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x))) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
	0.6b	(fma.f64 (pow.f64 (hypot.f64 x x) 1/8) (*.f64 (pow.f64 (hypot.f64 x x) 3/4) (pow.f64 (hypot.f64 x x) 1/8)) 0)
▶	0.4b	(/.f64 (pow.f64 (hypot.f64 x x) 3/4) (/.f64 1 (pow.f64 (hypot.f64 x x) 1/4)))

Compiler

Compiled 6875 to 3611 computations (47.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.2b	(/.f64 1 (pow.f64 (hypot.f64 x x) 1/4))
✓	0.3b	(/.f64 (pow.f64 (hypot.f64 x x) 3/4) (/.f64 1 (pow.f64 (hypot.f64 x x) 1/4)))

series402.0ms (13.2%)

Counts

3 → 36

Calls

3 calls:

205.0ms	(pow.f64 (hypot.f64 x x) 3/4)
193.0ms	(/.f64 1 (pow.f64 (hypot.f64 x x) 1/4))
4.0ms	(/.f64 (pow.f64 (hypot.f64 x x) 3/4) (/.f64 1 (pow.f64 (hypot.f64 x x) 1/4)))

rewrite61.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

758×	`log1p-expm1-u_binary64`
758×	`expm1-log1p-u_binary64`
170×	`prod-diff_binary64`
117×	`egg-rr`
86×	`add-sqr-sqrt_binary64`

Counts

3 → 117

Calls

3 calls:

59.0ms	(pow.f64 (hypot.f64 x x) 3/4)
59.0ms	(/.f64 1 (pow.f64 (hypot.f64 x x) 1/4))
59.0ms	(/.f64 (pow.f64 (hypot.f64 x x) 3/4) (/.f64 1 (pow.f64 (hypot.f64 x x) 1/4)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	232	18
2	2268	18
3	5104	18
0	0	0
1	0	0

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

594×	`exp-prod_binary64`
469×	`fma-neg_binary64`
439×	`fma-def_binary64`
325×	`rules-20_binary64`
311×	`exp-diff_binary64`

Counts

153 → 130

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	492
1	84	488
2	177	428
3	453	340
4	1353	312
5	4255	312
6	5105	312

prune162.0ms (5.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	242	9	251

Error

Counts

251 → 9

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	40.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	33.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.6b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	0.9b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3))
	0.4b	(*.f64 (pow.f64 (hypot.f64 x x) 3/4) (/.f64 1 (pow.f64 (hypot.f64 x x) -1/4)))
	0.7b	(/.f64 (pow.f64 (hypot.f64 x x) 3/4) (*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/8) -1) (pow.f64 (pow.f64 (hypot.f64 x x) 1/8) -1)))
✓	0.4b	(/.f64 (pow.f64 (hypot.f64 x x) 3/4) (/.f64 1 (pow.f64 (hypot.f64 x x) 1/4)))

Compiler

Compiled 4290 to 2390 computations (44.3% saved)

regimes176.0ms (5.7%)

Accuracy

Total 0.1b remaining (83.5%)

Threshold costs 0.1b (83.5%)

Counts

52 → 1

Compiler

Compiled 2577 to 1722 computations (33.2% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end103.0ms (3.4%)

Compiler: Compiled 108 to 71 computations (34.3% saved)

Details

analyze4.0ms (0.1%)

sample823.0ms (26.9%)

simplify86.0ms (2.8%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite38.0ms (1.2%)

simplify44.0ms (1.4%)

prune26.0ms (0.8%)

localize4.0ms (0.1%)

series18.0ms (0.6%)

rewrite92.0ms (3%)

simplify10.0ms (0.3%)

prune108.0ms (3.5%)

localize7.0ms (0.2%)

series430.0ms (14.1%)

rewrite127.0ms (4.2%)

simplify45.0ms (1.5%)

prune208.0ms (6.8%)

localize10.0ms (0.3%)

series402.0ms (13.2%)

rewrite61.0ms (2%)

simplify65.0ms (2.1%)

prune162.0ms (5.3%)

regimes176.0ms (5.7%)

simplify1.0ms (0%)

end103.0ms (3.4%)

Profiling