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)

sample935.0ms (31%)

Results

906.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify7.0ms (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)

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)

simplify166.0ms (5.5%)

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

prune11.0ms (0.3%)

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
	32.7b	(*.f64 (sqrt.f64 2) x)
▶	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)))
	42.8b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 203 to 91 computations (55.2% 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)))

series15.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

11.0ms	(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))

simplify79.0ms (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

prune73.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	124	8	132

Error

0.0b

Counts

132 → 8

Alt Table

Status	Error	Program
	32.7b	(*.f64 (sqrt.f64 2) x)
▶	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.1b	(hypot.f64 x x)
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	42.8b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1790 to 458 computations (74.4% 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	(sqrt.f64 (hypot.f64 x x))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

series470.0ms (15.6%)

Counts

3 → 36

Calls

3 calls:

243.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
222.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`sqrt-prod_binary64`
69×	`add-sqr-sqrt_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`
24×	`associate-r_binary64`

Counts

3 → 135

Calls

3 calls:

10.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
3.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
1.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify129.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

569×	`unswap-sqr_binary64`
453×	`exp-prod_binary64`
451×	`sqr-pow_binary64`
387×	`log-prod_binary64`
386×	`*-commutative_binary64`

Counts

171 → 131

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	2417
1	238	2133
2	797	1880
3	1496	1751
4	3366	1674
5	4592	1674
6	4857	1674

prune99.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	190	9	199

Error

0.0b

Counts

199 → 9

Alt Table

Status	Error	Program
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.1b	(hypot.f64 x x)
	32.7b	(*.f64 (sqrt.f64 2) x)
▶	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 3/4))
	0.9b	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 5/2) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)))
	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)))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 7/2))
	42.8b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))
	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 3633 to 1205 computations (66.8% saved)

localize8.0ms (0.3%)

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))
✓	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 3/4))

series230.0ms (7.6%)

Counts

2 → 24

Calls

2 calls:

225.0ms	(pow.f64 (hypot.f64 x x) 3/4)
4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 3/4))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
9×	`associate-l_binary64`
9×	`unswap-sqr_binary64`
9×	`unpow-prod-down_binary64`

Counts

2 → 61

Calls

2 calls:

8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 3/4))
1.0ms	(pow.f64 (hypot.f64 x x) 3/4)

simplify120.0ms (4%)

Algorithm

1×	egg-herbie

Rules

401×	`*-commutative_binary64`
396×	`sqr-pow_binary64`
291×	`associate-l_binary64`
258×	`fma-neg_binary64`
248×	`associate-r_binary64`

Counts

85 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	96	1437
1	183	1403
2	429	1367
3	1147	1273
4	1896	1203
5	3739	1175
6	4726	1175
7	4977	1175
8	4881	1175

prune98.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	129	8	137

Error

Counts

137 → 8

Alt Table

Status	Error	Program
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.1b	(hypot.f64 x x)
	32.7b	(*.f64 (sqrt.f64 2) x)
	0.6b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))) (pow.f64 (hypot.f64 x x) 3/4))
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	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)))
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 7/2))
	42.8b	(cbrt.f64 (.f64 (.f64 (hypot.f64 x x) (hypot.f64 x x)) (hypot.f64 x x)))

Compiler

Compiled 2269 to 928 computations (59.1% saved)

regimes404.0ms (13.4%)

Accuracy

Total 0.1b remaining (75.5%)

Threshold costs 0.1b (75.5%)

Counts

133 → 1

Compiler

Compiled 7546 to 4140 computations (45.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end93.0ms (3.1%)

Compiler: Compiled 113 to 60 computations (46.9% saved)

Details

analyze4.0ms (0.1%)

sample935.0ms (31%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify166.0ms (5.5%)

prune11.0ms (0.3%)

localize4.0ms (0.1%)

series15.0ms (0.5%)

rewrite10.0ms (0.3%)

simplify79.0ms (2.6%)

prune73.0ms (2.4%)

localize6.0ms (0.2%)

series470.0ms (15.6%)

rewrite26.0ms (0.9%)

simplify129.0ms (4.3%)

prune99.0ms (3.3%)

localize8.0ms (0.3%)

series230.0ms (7.6%)

rewrite13.0ms (0.4%)

simplify120.0ms (4%)

prune98.0ms (3.3%)

regimes404.0ms (13.4%)

simplify2.0ms (0.1%)

end93.0ms (3.1%)

Profiling