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)

sample827.0ms (28.2%)

Results

797.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify6.0ms (0.2%)

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)

localize3.0ms (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)

simplify159.0ms (5.4%)

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

prune10.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Error

0.1b

Counts

16 → 5

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	33.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 177 to 81 computations (54.2% saved)

localize4.0ms (0.1%)

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

series16.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

12.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite10.0ms (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:

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

simplify75.0ms (2.6%)

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

prune75.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	122	9	131

Error

0.0b

Counts

131 → 9

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	33.5b	(*.f64 (sqrt.f64 2) x)
▶	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	1.3b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 1850 to 478 computations (74.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

series616.0ms (21%)

Counts

3 → 36

Calls

3 calls:

380.0ms

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

232.0ms

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

4.0ms

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

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`sqrt-pow1_binary64`
51×	`pow1_binary64`
47×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
36×	`pow-prod-up_binary64`

Counts

3 → 121

Calls

3 calls:

13.0ms

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

6.0ms

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

1.0ms

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

simplify109.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
340×	`unswap-sqr_binary64`
272×	`exp-sum_binary64`
265×	`distribute-rgt-in_binary64`
219×	`fma-neg_binary64`

Counts

157 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1915
1	224	1702
2	445	1614
3	843	1530
4	2021	1476
5	4741	1476
6	4949	1476

prune117.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	226	9	235

Error

0.0b

Counts

235 → 9

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	0.9b	(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.0b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (fabs.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	0.9b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 4)
▶	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))

Compiler

Compiled 4608 to 1137 computations (75.3% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series16.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

12.0ms

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

4.0ms

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

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`sqrt-prod_binary64`
83×	`sqrt-pow1_binary64`
78×	`add-sqr-sqrt_binary64`
63×	`pow1_binary64`
43×	`pow1/2_binary64`

Counts

2 → 137

Calls

2 calls:

12.0ms

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

8.0ms

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

simplify116.0ms (4%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
529×	`unswap-sqr_binary64`
412×	`log-prod_binary64`
374×	`associate-l_binary64`
354×	`*-commutative_binary64`

Counts

149 → 141

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	88	1211
1	125	1136
2	352	1110
3	1036	1074
4	2170	1074
5	3751	1065
6	4436	1065
7	4906	1065

prune128.0ms (4.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	241	10	251

Error

0.0b

Counts

251 → 10

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.7b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) 3)))
	0.9b	(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	0.9b	(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	1.0b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (fabs.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	0.9b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 4)

Compiler

Compiled 4784 to 1208 computations (74.7% saved)

regimes440.0ms (15%)

Accuracy

Total 0.1b remaining (85.9%)

Threshold costs 0.1b (85.9%)

Counts

140 → 1

Compiler

Compiled 8138 to 4436 computations (45.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end109.0ms (3.7%)

Compiler: Compiled 152 to 70 computations (53.9% saved)

Details

analyze4.0ms (0.1%)

sample827.0ms (28.2%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify159.0ms (5.4%)

prune10.0ms (0.3%)

localize4.0ms (0.1%)

series16.0ms (0.5%)

rewrite10.0ms (0.3%)

simplify75.0ms (2.6%)

prune75.0ms (2.6%)

localize6.0ms (0.2%)

series616.0ms (21%)

rewrite32.0ms (1.1%)

simplify109.0ms (3.7%)

prune117.0ms (4%)

localize6.0ms (0.2%)

series16.0ms (0.5%)

rewrite36.0ms (1.2%)

simplify116.0ms (4%)

prune128.0ms (4.4%)

regimes440.0ms (15%)

simplify2.0ms (0.1%)

end109.0ms (3.7%)

Profiling