Details

analyze13.0ms (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)

sample1.4s (31.3%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify118.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1333×	`fma-def_binary64`
773×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
453×	`associate-l_binary64`
451×	`count-2_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	25	4
3	46	4
4	98	4
5	245	4
6	763	4
7	1382	4
8	2673	4
9	3450	4
10	4144	4
11	4482	4
12	4395	4
13	4766	4
14	4993	4
15	4742	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 12 computations (40% saved)

localize2.0ms (0%)

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)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot.f64 x x)

simplify161.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
575×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	159
1	29	150
2	46	150
3	52	150
4	61	150
5	88	150
6	119	150
7	178	150
8	376	150
9	696	150
10	701	150
11	875	150
12	1086	150
13	1314	150
14	1571	150
15	1876	150
16	2224	150
17	2699	150
18	3317	150
19	3513	150
20	3687	150
21	3801	150
22	3848	150
23	3900	150
24	4778	150
25	4863	150
26	4688	150

prune9.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.0b

Counts

16 → 4

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	32.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.3b	(*.f64 (sqrt.f64 2) x)
▶	1.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 157 to 73 computations (53.5% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series531.0ms (12.2%)

Counts

3 → 36

Calls

3 calls:

289.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
238.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify217.0ms (5%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
501×	`exp-prod_binary64`
410×	`exp-sum_binary64`
358×	`div-exp_binary64`
330×	`fma-neg_binary64`

Counts

129 → 123

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	103	1636
1	196	1516
2	428	1327
3	1121	1221
4	2365	953
5	4247	953
6	4195	953
7	4661	953
8	5307	953

prune72.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	205	5	210

Error

0.0b

Counts

210 → 5

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	32.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.3b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 3753 to 821 computations (78.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
✓	0.4b	(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
	0.6b	(cbrt.f64 (hypot.f64 x x))

series303.0ms (7%)

Counts

3 → 24

Calls

3 calls:

290.0ms

(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

9.0ms

(sqrt.f64 (hypot.f64 x x))

4.0ms

(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
19×	`sqrt-prod_binary64`
15×	`pow1_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`

Counts

3 → 81

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

8.0ms

(*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

1.0ms

(sqrt.f64 (hypot.f64 x x))

simplify167.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-neg_binary64`
360×	`exp-sum_binary64`
306×	`exp-prod_binary64`
302×	`fma-def_binary64`
291×	`exp-diff_binary64`

Counts

105 → 116

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	107	1916
1	218	1671
2	553	1620
3	852	1599
4	1530	1259
5	3104	1080
6	3958	1080
7	4945	1080
8	5000	1080

prune55.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	154	5	159

Error

0.0b

Counts

159 → 5

Alt Table

Status	Error	Program
✓	0.8b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	32.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.3b	(*.f64 (sqrt.f64 2) x)
▶	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 3046 to 678 computations (77.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.7b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)

series802.0ms (18.4%)

Counts

3 → 36

Calls

3 calls:

591.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
206.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
4.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
20×	`cbrt-prod_binary64`
18×	`unpow-prod-down_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 90

Calls

3 calls:

7.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
2.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
1.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))

simplify113.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
538×	`unswap-sqr_binary64`
377×	`associate-l_binary64`
330×	`log-prod_binary64`
309×	`associate-r_binary64`

Counts

126 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	2231
1	240	2176
2	544	2108
3	1495	1616
4	2906	1590
5	4489	1590
6	4972	1590

prune74.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	1.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.8b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	32.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.3b	(*.f64 (sqrt.f64 2) x)
✓	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.5b	(.f64 (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 3011 to 1083 computations (64% saved)

regimes192.0ms (4.4%)

Accuracy

Total 0.1b remaining (70.4%)

Threshold costs 0.1b (70.4%)

Counts

43 → 1

Compiler

Compiled 2722 to 1298 computations (52.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end79.0ms (1.8%)

Compiler: Compiled 100 to 47 computations (53% saved)

Details

analyze13.0ms (0.3%)

sample1.4s (31.3%)

simplify118.0ms (2.7%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify161.0ms (3.7%)

prune9.0ms (0.2%)

localize5.0ms (0.1%)

series531.0ms (12.2%)

rewrite17.0ms (0.4%)

simplify217.0ms (5%)

prune72.0ms (1.7%)

localize7.0ms (0.2%)

series303.0ms (7%)

rewrite21.0ms (0.5%)

simplify167.0ms (3.8%)

prune55.0ms (1.3%)

localize8.0ms (0.2%)

series802.0ms (18.4%)

rewrite15.0ms (0.3%)

simplify113.0ms (2.6%)

prune74.0ms (1.7%)

regimes192.0ms (4.4%)

simplify2.0ms (0%)

end79.0ms (1.8%)

Profiling