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)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 20 to 10 computations (50% 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

prune5.0ms (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)

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

prune10.0ms (0.2%)

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)
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
	40.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	35.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	27.5b	(*.f64 (sqrt.f64 2) x)

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)))

series14.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(sqrt.f64 (hypot.f64 x x))
5.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite10.0ms (0.2%)

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 (1.7%)

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

prune73.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	125	7	132

Error

Counts

132 → 7

Alt Table

Status	Error	Program
	35.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.1b	(hypot.f64 x x)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x 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))))
	1.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	27.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1822 to 452 computations (75.2% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series561.0ms (12.8%)

Counts

3 → 36

Calls

3 calls:

328.0ms

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

228.0ms

(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))))

rewrite31.0ms (0.7%)

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))))

7.0ms

(*.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)))

simplify102.0ms (2.3%)

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 → 154

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	2107
1	224	1834
2	445	1614
3	843	1530
4	2021	1476
5	4741	1476
6	4949	1476

prune137.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	234	6	240

Error

Counts

240 → 6

Alt Table

Status	Error	Program
	35.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.1b	(hypot.f64 x x)
▶	1.0b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))
	27.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 4726 to 1077 computations (77.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)))
✓	0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)
✓	0.5b	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2))

series1.5s (34.9%)

Counts

3 → 36

Calls

3 calls:

1.2s

(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)

322.0ms

(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2))

4.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`sqrt-prod_binary64`
87×	`unpow-prod-down_binary64`
81×	`add-sqr-sqrt_binary64`
39×	`add-exp-log_binary64`
28×	`unswap-sqr_binary64`

Counts

3 → 162

Calls

3 calls:

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)))

10.0ms

(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2))

3.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)

simplify146.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

396×	`exp-prod_binary64`
363×	`*-commutative_binary64`
325×	`unswap-sqr_binary64`
319×	`log-prod_binary64`
306×	`exp-sum_binary64`

Counts

198 → 180

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	170	4099
1	330	3496
2	1032	3307
3	1934	2878
4	4165	2870
5	4945	2870

prune155.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	273	6	279

Error

Counts

279 → 6

Alt Table

Status	Error	Program
	35.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	1.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3/2)))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))))
	27.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 7261 to 2482 computations (65.8% saved)

regimes735.0ms (16.8%)

Accuracy

Total 0.1b remaining (70.7%)

Threshold costs 0.1b (70.7%)

Counts

194 → 1

Compiler

Compiled 12802 to 6384 computations (50.1% saved)

simplify2.0ms (0%)

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)

sample529.0ms (12.1%)

Algorithm

1×

intervals

Results

247.0ms

8000×

body

128

valid

Compiler

Compiled 104 to 45 computations (56.7% saved)

Details

analyze4.0ms (0.1%)

sample30.0ms (0.7%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize2.0ms (0%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify161.0ms (3.7%)

prune10.0ms (0.2%)

localize4.0ms (0.1%)

series14.0ms (0.3%)

rewrite10.0ms (0.2%)

simplify75.0ms (1.7%)

prune73.0ms (1.7%)

localize6.0ms (0.1%)

series561.0ms (12.8%)

rewrite31.0ms (0.7%)

simplify102.0ms (2.3%)

prune137.0ms (3.1%)

localize9.0ms (0.2%)

series1.5s (34.9%)

rewrite42.0ms (1%)

simplify146.0ms (3.3%)

prune155.0ms (3.5%)

regimes735.0ms (16.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample529.0ms (12.1%)

Profiling