Details

analyze161.0ms (4.9%)

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)

sample44.0ms (1.3%)

Algorithm

1×

intervals

Results

37.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify132.0ms (4%)

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 (0.1%)

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)

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 (5.1%)

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

prune128.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	10	5	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	6	16

Error

0.0b

Counts

16 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.3b	(*.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)))
	41.5b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))

Compiler

Compiled 191 to 91 computations (52.4% 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	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series27.0ms (0.8%)

Counts

2 → 12

Calls

2 calls:

23.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

6.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))

simplify147.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
308×	`sqr-pow_binary64`
263×	`associate-+l+_binary64`
259×	`associate-/l*_binary64`

Counts

80 → 79

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	54	643
1	79	602
2	190	589
3	392	554
4	718	554
5	1343	554
6	2541	540
7	4570	540
8	5161	540

prune102.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	125	7	132

Error

0.0b

Counts

132 → 7

Alt Table

Status	Error	Program
▶	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	41.6b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 1766 to 438 computations (75.2% saved)

localize49.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.5b	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
✓	0.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series497.0ms (15.1%)

Counts

4 → 36

Calls

4 calls:

268.0ms	(cbrt.f64 (hypot.f64 x x))
213.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
11.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
5.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`

Counts

4 → 89

Calls

4 calls:

6.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
5.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
1.0ms	(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify125.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

459×	`unswap-sqr_binary64`
433×	`fma-def_binary64`
360×	`fma-neg_binary64`
325×	`*-commutative_binary64`
311×	`sqr-pow_binary64`

Counts

125 → 138

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	2157
1	208	1998
2	536	1829
3	923	1329
4	1177	1298
5	2456	1298
6	4266	1298
7	4938	1298

prune49.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	138	7	145

Error

0.0b

Counts

145 → 7

Alt Table

Status	Error	Program
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.3b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	41.5b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (hypot.f64 x x) (sqrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 2796 to 563 computations (79.9% 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 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
	0.6b	(cbrt.f64 (hypot.f64 x x))

series246.0ms (7.5%)

Counts

2 → 24

Calls

2 calls:

242.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
4.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
16×	`unpow-prod-down_binary64`
11×	`associate-l_binary64`
10×	`unswap-sqr_binary64`

Counts

2 → 69

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
2.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)

simplify85.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

460×	`*-commutative_binary64`
438×	`fma-def_binary64`
341×	`exp-prod_binary64`
269×	`sqr-pow_binary64`
261×	`distribute-rgt-in_binary64`

Counts

93 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	1249
1	200	1027
2	409	991
3	1324	892
4	2150	818
5	4155	818
6	4785	818

prune68.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	3	3
Picked	0	1	1
Done	1	2	3
Total	171	7	178

Error

Counts

178 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	31.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.3b	(*.f64 (sqrt.f64 2) x)
	1.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	41.5b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (.f64 (hypot.f64 x x) (sqrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 2837 to 1038 computations (63.4% saved)

regimes138.0ms (4.2%)

Accuracy

Total 0.1b remaining (75.9%)

Threshold costs 0.1b (75.9%)

Counts

42 → 1

Compiler

Compiled 2738 to 1330 computations (51.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

sample1.1s (32.2%)

Algorithm

1×

intervals

Results

677.0ms

8000×

body

128

valid

Compiler

Compiled 98 to 51 computations (48% saved)

Details

analyze161.0ms (4.9%)

sample44.0ms (1.3%)

simplify132.0ms (4%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify167.0ms (5.1%)

prune128.0ms (3.9%)

localize4.0ms (0.1%)

series27.0ms (0.8%)

rewrite11.0ms (0.3%)

simplify147.0ms (4.5%)

prune102.0ms (3.1%)

localize49.0ms (1.5%)

series497.0ms (15.1%)

rewrite18.0ms (0.6%)

simplify125.0ms (3.8%)

prune49.0ms (1.5%)

localize5.0ms (0.2%)

series246.0ms (7.5%)

rewrite13.0ms (0.4%)

simplify85.0ms (2.6%)

prune68.0ms (2.1%)

regimes138.0ms (4.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (32.2%)

Profiling