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)

sample792.0ms (25.9%)

Results

764.0ms	8256×	body	128	valid
0.0ms	3×	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)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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)

simplify158.0ms (5.2%)

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 (0.4%)

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
▶	0.5b	(*.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)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x 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)))

series12.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

9.0ms	(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))

simplify76.0ms (2.5%)

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

prune51.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	125	7	132

Error

0.0b

Counts

132 → 7

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
▶	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.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)))

Compiler

Compiled 1712 to 434 computations (74.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)

series1.0s (33.6%)

Counts

4 → 48

Calls

4 calls:

568.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
251.0ms	(cbrt.f64 (hypot.f64 x x))
205.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
4.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
20×	`sqrt-prod_binary64`
18×	`unpow-prod-down_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

6.0ms	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
2.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2)
1.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify127.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
542×	`unswap-sqr_binary64`
388×	`associate-l_binary64`
354×	`log-prod_binary64`
328×	`sqr-pow_binary64`

Counts

151 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	134	2505
1	264	2445
2	586	2357
3	1596	1776
4	3150	1734
5	4609	1734
6	4856	1734

prune83.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	166	9	175

Error

0.0b

Counts

175 → 9

Alt Table

Status	Error	Program
▶	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	2.2b	(.f64 (.f64 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	2.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))))
	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/4)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 3138 to 1163 computations (62.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.4b	(*.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)
	0.5b	(cbrt.f64 (hypot.f64 x x))

series211.0ms (6.9%)

Counts

2 → 24

Calls

2 calls:

207.0ms	(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)))

rewrite16.0ms (0.5%)

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:

10.0ms	(*.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)

simplify84.0ms (2.7%)

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

prune70.0ms (2.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	171	9	180

Error

0.0b

Counts

180 → 9

Alt Table

Status	Error	Program
✓	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
	2.2b	(.f64 (.f64 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 5/2) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 5/2)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	44.0b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	29.9b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.1b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	2.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (hypot.f64 x x))))))
	1.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/4)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))

Compiler

Compiled 2861 to 1055 computations (63.1% saved)

regimes167.0ms (5.5%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

49 → 1

Compiler

Compiled 2734 to 1596 computations (41.6% 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 (3.5%)

Compiler: Compiled 115 to 61 computations (47% saved)

Details

analyze4.0ms (0.1%)

sample792.0ms (25.9%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify158.0ms (5.2%)

prune11.0ms (0.4%)

localize4.0ms (0.1%)

series12.0ms (0.4%)

rewrite10.0ms (0.3%)

simplify76.0ms (2.5%)

prune51.0ms (1.7%)

localize9.0ms (0.3%)

series1.0s (33.6%)

rewrite17.0ms (0.6%)

simplify127.0ms (4.1%)

prune83.0ms (2.7%)

localize6.0ms (0.2%)

series211.0ms (6.9%)

rewrite16.0ms (0.5%)

simplify84.0ms (2.7%)

prune70.0ms (2.3%)

regimes167.0ms (5.5%)

simplify2.0ms (0.1%)

end109.0ms (3.5%)

Profiling