Details

analyze4.0ms (0.2%)

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)

sample820.0ms (31.9%)

Results

793.0ms

8256×

body

128

valid

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)

series6.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(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)

simplify162.0ms (6.3%)

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

prune9.0ms (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

0.0b

Counts

16 → 5

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)))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.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	(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)))

series42.0ms (1.6%)

Counts

2 → 12

Calls

2 calls:

38.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite9.0ms (0.4%)

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 (3%)

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

prune59.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	124	7	131

Error

0.0b

Counts

131 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	17.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
▶	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1750 to 440 computations (74.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series404.0ms (15.7%)

Counts

3 → 36

Calls

3 calls:

211.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
190.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

rewrite25.0ms (1%)

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)
3.0ms	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify118.0ms (4.6%)

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

prune78.0ms (3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	191	7	198

Error

0.0b

Counts

198 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	17.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
▶	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 3547 to 1148 computations (67.6% saved)

localize7.0ms (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 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.5b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series373.0ms (14.5%)

Counts

4 → 36

Calls

4 calls:

182.0ms	(cbrt.f64 (hypot.f64 x x))
180.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
7.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
4.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
19×	`sqrt-prod_binary64`
18×	`cbrt-prod_binary64`
16×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 96

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
5.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
1.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
1.0ms	(cbrt.f64 (hypot.f64 x x))

simplify108.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

415×	`fma-def_binary64`
380×	`fma-neg_binary64`
331×	`unswap-sqr_binary64`
288×	`sqr-pow_binary64`
251×	`*-commutative_binary64`

Counts

132 → 136

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	2082
1	206	1889
2	505	1828
3	791	1342
4	1145	1310
5	2308	1310
6	4584	1310
7	4875	1310

prune57.0ms (2.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	156	7	163

Error

0.0b

Counts

163 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	17.6b	(.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
✓	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
✓	0.9b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 3058 to 677 computations (77.9% saved)

regimes103.0ms (4%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Counts

31 → 1

Compiler

Compiled 1782 to 876 computations (50.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end67.0ms (2.6%)

Compiler: Compiled 84 to 40 computations (52.4% saved)

Details

analyze4.0ms (0.2%)

sample820.0ms (31.9%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify162.0ms (6.3%)

prune9.0ms (0.3%)

localize4.0ms (0.1%)

series42.0ms (1.6%)

rewrite9.0ms (0.4%)

simplify76.0ms (3%)

prune59.0ms (2.3%)

localize6.0ms (0.2%)

series404.0ms (15.7%)

rewrite25.0ms (1%)

simplify118.0ms (4.6%)

prune78.0ms (3%)

localize7.0ms (0.3%)

series373.0ms (14.5%)

rewrite19.0ms (0.7%)

simplify108.0ms (4.2%)

prune57.0ms (2.2%)

regimes103.0ms (4%)

simplify2.0ms (0.1%)

end67.0ms (2.6%)

Profiling