Details

analyze1.4s (25%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample1.4s (24.9%)

Results

1.4s	8256×	body	128	valid
2.0ms	4×	body	8192	exit

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	15	4
4	15	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%)

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)

simplify167.0ms (2.9%)

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

prune8.0ms (0.1%)

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
▶	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 157 to 73 computations (53.5% saved)

localize7.0ms (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))

series564.0ms (9.9%)

Counts

3 → 36

Calls

3 calls:

323.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
236.0ms	(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)))

rewrite19.0ms (0.3%)

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:

8.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
5.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify133.0ms (2.4%)

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

prune67.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	204	6	210

Error

0.0b

Counts

210 → 6

Alt Table

Status	Error	Program
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)
▶	1.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 3797 to 835 computations (78% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series555.0ms (9.8%)

Counts

3 → 36

Calls

3 calls:

327.0ms

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

224.0ms

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

4.0ms

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

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`sqrt-prod_binary64`
12×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

7.0ms

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

6.0ms

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

1.0ms

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

simplify116.0ms (2%)

Algorithm

1×	egg-herbie

Rules

610×	`unswap-sqr_binary64`
430×	`exp-sum_binary64`
427×	`fma-def_binary64`
385×	`exp-prod_binary64`
285×	`*-commutative_binary64`

Counts

111 → 111

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	113	2056
1	234	1636
2	629	1544
3	1143	1262
4	1948	1262
5	4509	1230
6	4593	1223
7	4865	1223

prune47.0ms (0.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	128	8	136

Error

0.0b

Counts

136 → 8

Alt Table

Status	Error	Program
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	1.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (hypot.f64 x x)))
	30.4b	(*.f64 (sqrt.f64 2) x)
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 2793 to 613 computations (78.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series654.0ms (11.5%)

Counts

2 → 24

Calls

2 calls:

332.0ms

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

322.0ms

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

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
46×	`sqrt-prod_binary64`
33×	`rem-sqrt-square_binary64`
30×	`cbrt-prod_binary64`
24×	`associate-l_binary64`

Counts

2 → 90

Calls

2 calls:

11.0ms

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

9.0ms

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

simplify176.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary64`
456×	`exp-prod_binary64`
445×	`exp-sum_binary64`
308×	`fma-neg_binary64`
299×	`unswap-sqr_binary64`

Counts

114 → 126

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	121	2470
1	274	2265
2	648	2139
3	1040	1788
4	2173	1719
5	4494	1701
6	4110	1671
7	4771	1671
8	4978	1671
9	4805	1671

prune69.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	189	8	197

Error

0.0b

Counts

197 → 8

Alt Table

Status	Error	Program
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	32.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	1.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (hypot.f64 x x)))
	30.4b	(*.f64 (sqrt.f64 2) x)
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 5370 to 1039 computations (80.7% saved)

regimes93.0ms (1.6%)

Accuracy

Total 0.1b remaining (74.5%)

Threshold costs 0.1b (74.5%)

Counts

29 → 1

Compiler

Compiled 1834 to 832 computations (54.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end85.0ms (1.5%)

Compiler: Compiled 129 to 55 computations (57.4% saved)

Details

analyze1.4s (25%)

sample1.4s (24.9%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify167.0ms (2.9%)

prune8.0ms (0.1%)

localize7.0ms (0.1%)

series564.0ms (9.9%)

rewrite19.0ms (0.3%)

simplify133.0ms (2.4%)

prune67.0ms (1.2%)

localize7.0ms (0.1%)

series555.0ms (9.8%)

rewrite19.0ms (0.3%)

simplify116.0ms (2%)

prune47.0ms (0.8%)

localize9.0ms (0.2%)

series654.0ms (11.5%)

rewrite29.0ms (0.5%)

simplify176.0ms (3.1%)

prune69.0ms (1.2%)

regimes93.0ms (1.6%)

simplify2.0ms (0%)

end85.0ms (1.5%)

Profiling