Details

analyze5.0ms (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)

sample868.0ms (33.2%)

Results

756.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify8.0ms (0.3%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(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
✓	0.2b	(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 (6.1%)

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

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
	31.8b	(*.f64 (sqrt.f64 2) x)
✓	0.2b	(hypot.f64 x x)
▶	0.6b	(*.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)))
	31.3b	(neg.f64 (*.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))
	0.2b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series14.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(sqrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite10.0ms (0.4%)

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))

simplify78.0ms (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

prune69.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	120	11	131

Error

Counts

131 → 11

Alt Table

Status	Error	Program
	31.8b	(*.f64 (sqrt.f64 2) x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.2b	(hypot.f64 x x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	18.9b	(.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)))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.6b	(*.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))))
	1.4b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (*.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)))))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1878 to 494 computations (73.7% 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)))
	0.2b	(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))))

series553.0ms (21.2%)

Counts

3 → 36

Calls

3 calls:

337.0ms

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

212.0ms

(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 (1.2%)

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)))

simplify96.0ms (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

prune157.0ms (6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	2	6	8
Picked	1	0	1
Done	1	1	2
Total	228	9	237

Error

Counts

237 → 9

Alt Table

Status	Error	Program
✓	0.2b	(hypot.f64 x x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.0b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 4)
	18.9b	(.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)))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.8b	(*.f64 (sqrt.f64 2) x)
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
▶	0.6b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 4575 to 1133 computations (75.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
	0.2b	(hypot.f64 x x)
✓	0.3b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2))

series31.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

27.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)
4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`sqrt-prod_binary64`
18×	`unpow-prod-down_binary64`
12×	`unswap-sqr_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 72

Calls

2 calls:

7.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2))
2.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2)

simplify117.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

614×	`unswap-sqr_binary64`
473×	`sqr-pow_binary64`
426×	`*-commutative_binary64`
348×	`log-prod_binary64`
319×	`associate-l_binary64`

Counts

84 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	1672
1	156	1592
2	396	947
3	1073	863
4	2150	803
5	3862	803
6	4993	803
7	4998	803
8	4924	803

prune74.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	146	9	155

Error

Counts

155 → 9

Alt Table

Status	Error	Program
✓	0.2b	(hypot.f64 x x)
	1.4b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
	1.0b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 4)
	18.9b	(.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)))))
	4.8b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 (hypot.f64 x x)))))
	31.8b	(*.f64 (sqrt.f64 2) x)
	1.0b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.6b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (hypot.f64 x x)) 3/2))
	31.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 2555 to 923 computations (63.9% saved)

regimes195.0ms (7.4%)

Accuracy

Total 0.1b remaining (80.8%)

Threshold costs 0.1b (80.8%)

Counts

57 → 1

Compiler

Compiled 3322 to 1692 computations (49.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end92.0ms (3.5%)

Compiler: Compiled 106 to 56 computations (47.2% saved)

Details

analyze5.0ms (0.2%)

sample868.0ms (33.2%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify161.0ms (6.1%)

prune11.0ms (0.4%)

localize4.0ms (0.1%)

series14.0ms (0.5%)

rewrite10.0ms (0.4%)

simplify78.0ms (3%)

prune69.0ms (2.6%)

localize6.0ms (0.2%)

series553.0ms (21.2%)

rewrite32.0ms (1.2%)

simplify96.0ms (3.7%)

prune157.0ms (6%)

localize7.0ms (0.3%)

series31.0ms (1.2%)

rewrite15.0ms (0.6%)

simplify117.0ms (4.5%)

prune74.0ms (2.8%)

regimes195.0ms (7.4%)

simplify2.0ms (0.1%)

end92.0ms (3.5%)

Profiling