Details

analyze6.0ms (0.3%)

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 8 computations (20% saved)

sample1.1s (56.2%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify35.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-def_binary64`
559×	`hypot-def_binary64`
544×	`distribute-rgt-out_binary64`
436×	`associate-l_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	30	4
3	53	4
4	121	4
5	361	4
6	1334	4
7	2593	4
8	3960	4
9	4922	4

Stop Event

1×	node limit

Counts

1 → 2

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 12 computations (40% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

13.0ms

(hypot.f64 x x)

rewrite27.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
227×	`add-cube-cbrt_binary64`
222×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	700	4

Stop Event

1×	node limit

Counts

1 → 40

Calls

1 calls:

27.0ms

(hypot.f64 x x)

simplify46.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

52 → 43

prune26.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	0.1b	(hypot.f64 x x)
	5.5b	(exp.f64 (log.f64 (hypot.f64 x x)))
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 469 to 223 computations (52.5% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series26.0ms (1.3%)

Counts

2 → 0

Calls

2 calls:

18.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
8.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite35.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
339×	`pow1_binary64`
263×	`unpow-prod-down_binary64`
191×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	124	10
2	1142	10

Stop Event

1×	node limit

Counts

2 → 88

Calls

2 calls:

34.0ms	(sqrt.f64 (hypot.f64 x x))
34.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

88 → 88

prune58.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	130	7	137

Error

0.0b

Counts

137 → 7

Alt Table

Status	Error	Program
	19.1b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)) 2)
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
▶	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	0.1b	(hypot.f64 x x)
	5.5b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 1557 to 826 computations (46.9% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series14.0ms (0.7%)

Counts

3 → 12

Calls

3 calls:

7.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
4.0ms	(cbrt.f64 (hypot.f64 x x))
3.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))

rewrite41.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`log1p-expm1-u_binary64`
439×	`expm1-log1p-u_binary64`
333×	`unpow-prod-down_binary64`
224×	`log-prod_binary64`
131×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	142	19
2	1333	19

Stop Event

1×	node limit

Counts

3 → 121

Calls

3 calls:

39.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
39.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
39.0ms	(cbrt.f64 (hypot.f64 x x))

simplify12.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

133 → 124

prune103.0ms (5.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	267	8	275

Error

0.0b

Counts

275 → 8

Alt Table

Status	Error	Program
	32.0b	(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x x))) 3/2)
✓	0.1b	(hypot.f64 x x)
	19.1b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)) 2)
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
✓	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	5.5b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 4771 to 1861 computations (61% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	5.6b	(exp.f64 (log.f64 (hypot.f64 x x)))

series167.0ms (8.2%)

Counts

2 → 24

Calls

2 calls:

163.0ms	(log.f64 (hypot.f64 x x))
4.0ms	(exp.f64 (log.f64 (hypot.f64 x x)))

rewrite37.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

311×	`log1p-expm1-u_binary64`
311×	`expm1-log1p-u_binary64`
275×	`add-log-exp_binary64`
274×	`add-exp-log_binary64`
272×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	81	10
2	887	10

Stop Event

1×	node limit

Counts

2 → 88

Calls

2 calls:

35.0ms	(log.f64 (hypot.f64 x x))
35.0ms	(exp.f64 (log.f64 (hypot.f64 x x)))

simplify24.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

139×	`fma-neg_binary64`
102×	`fma-def_binary64`
37×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`
33×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	212
1	34	212
2	58	212
3	111	212
4	211	212
5	325	212
6	422	212
7	572	212
8	651	212
9	684	212

Stop Event

1×

saturated

Counts

112 → 94

prune46.0ms (2.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	137	8	145

Error

0.0b

Counts

145 → 8

Alt Table

Status	Error	Program
	32.0b	(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x x))) 3/2)
✓	0.1b	(hypot.f64 x x)
	19.1b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)) 2)
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
✓	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	5.5b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 1563 to 663 computations (57.6% saved)

regimes66.0ms (3.2%)

Accuracy

Total 0.1b remaining (75.8%)

Threshold costs 0.1b (75.8%)

Counts

18 → 1

Compiler

Compiled 626 to 438 computations (30% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4

Stop Event

1×

saturated

end79.0ms (3.9%)

Compiler: Compiled 70 to 45 computations (35.7% saved)

Iter	Nodes	Cost
0	17	212
1	34	212
2	58	212
3	111	212
4	211	212
5	325	212
6	422	212
7	572	212
8	651	212
9	684	212

Iter	Nodes	Cost
0	17	212
1	34	212
2	58	212
3	111	212
4	211	212
5	325	212
6	422	212
7	572	212
8	651	212
9	684	212

Details

analyze6.0ms (0.3%)

sample1.1s (56.2%)

simplify35.0ms (1.7%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series13.0ms (0.6%)

rewrite27.0ms (1.3%)

simplify46.0ms (2.3%)

prune26.0ms (1.3%)

localize7.0ms (0.4%)

series26.0ms (1.3%)

rewrite35.0ms (1.7%)

simplify6.0ms (0.3%)

prune58.0ms (2.8%)

localize5.0ms (0.2%)

series14.0ms (0.7%)

rewrite41.0ms (2%)

simplify12.0ms (0.6%)

prune103.0ms (5.1%)

localize6.0ms (0.3%)

series167.0ms (8.2%)

rewrite37.0ms (1.8%)

simplify24.0ms (1.2%)

prune46.0ms (2.2%)

regimes66.0ms (3.2%)

simplify2.0ms (0.1%)

end79.0ms (3.9%)

Profiling

Iter	Nodes	Cost
0	17	212
1	34	212
2	58	212
3	111	212
4	211	212
5	325	212
6	422	212
7	572	212
8	651	212
9	684	212