Details

analyze1.5s (33.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.1s (24.3%)

Results

933.0ms	8256×	body	128	valid
1.0ms	2×	body	8192	exit

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify139.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	22	9
3	41	9
4	88	9
5	221	9
6	693	9
7	1098	9
8	1100	9
9	1248	9
10	1418	9
11	1600	9
12	1825	9
13	2110	9
14	2529	9
15	3094	9
16	3780	9
17	3998	9
18	4242	9
19	4324	9
20	4357	9
21	4378	9
22	4947	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

30.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 x 2))
✓	29.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

series6.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
3.0ms	(*.f64 2 (pow.f64 x 2))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(*.f64 2 (pow.f64 x 2))
2.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

823×	`unswap-sqr_binary64`
448×	`hypot-def_binary64`
432×	`*-commutative_binary64`
402×	`sqr-pow_binary64`
358×	`times-frac_binary64`

Counts

53 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	490
1	110	449
2	247	437
3	826	431
4	1358	371
5	3482	371
6	4011	371
7	4935	371
8	4869	371

prune44.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	9	67

Error

0.1b

Counts

67 → 9

Alt Table

Status	Error	Program
	30.6b	(sqrt.f64 (.f64 (.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))))
	28.7b	(*.f64 (sqrt.f64 2) x)
✓	30.2b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	33.1b	(log1p.f64 (expm1.f64 (hypot.f64 x x)))
	34.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
	43.9b	(sqrt.f64 (*.f64 (+.f64 x x) (pow.f64 (sqrt.f64 x) 2)))
▶	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)))

Compiler

Compiled 853 to 625 computations (26.7% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series17.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))
0.0ms	(hypot.f64 x x)

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
308×	`sqr-pow_binary64`
263×	`associate-+l+_binary64`
259×	`associate-/l*_binary64`

Counts

102 → 83

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	61	802
1	85	752
2	199	739
3	402	701
4	728	701
5	1353	701
6	2551	685
7	4580	685
8	5171	685

prune164.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	5	2	7
Picked	1	0	1
Done	1	0	1
Total	107	6	113

Error

0.0b

Counts

113 → 6

Alt Table

Status	Error	Program
	30.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
▶	0.1b	(hypot.f64 x x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.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))))
	28.7b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 1494 to 368 computations (75.4% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

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

prune99.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	4	6	10

Error

0.0b

Counts

10 → 6

Alt Table

Status	Error	Program
	30.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
✓	0.1b	(hypot.f64 x x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.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))))
	28.7b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 171 to 82 computations (52% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series493.0ms (10.8%)

Counts

2 → 24

Calls

2 calls:

489.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (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))))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-pow1_binary64`
48×	`pow1_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`sqrt-prod_binary64`
36×	`pow-prod-up_binary64`

Counts

2 → 100

Calls

2 calls:

14.0ms	(.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)))

simplify105.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
338×	`fma-neg_binary64`
322×	`unswap-sqr_binary64`
245×	`exp-prod_binary64`
220×	`exp-sum_binary64`

Counts

124 → 126

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	100	1686
1	192	1428
2	410	1242
3	724	1206
4	1739	1160
5	4430	1156
6	4990	1156
7	4843	1156

prune92.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	188	7	195

Error

0.0b

Counts

195 → 7

Alt Table

Status	Error	Program
	30.4b	(sqrt.f64 (.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2))))
✓	0.1b	(hypot.f64 x x)
	0.8b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
	28.7b	(*.f64 (sqrt.f64 2) x)
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 3759 to 844 computations (77.5% saved)

regimes464.0ms (10.1%)

Accuracy

Total 0.1b remaining (72.8%)

Threshold costs 0.1b (72.8%)

Counts

91 → 1

Compiler

Compiled 5329 to 3139 computations (41.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	7	4
2	6	4

end83.0ms (1.8%)

Compiler: Compiled 107 to 48 computations (55.1% saved)

Details

analyze1.5s (33.2%)

sample1.1s (24.3%)

simplify139.0ms (3%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite8.0ms (0.2%)

simplify87.0ms (1.9%)

prune44.0ms (1%)

localize4.0ms (0.1%)

series17.0ms (0.4%)

rewrite11.0ms (0.3%)

simplify85.0ms (1.9%)

prune164.0ms (3.6%)

localize2.0ms (0%)

prune99.0ms (2.2%)

localize6.0ms (0.1%)

series493.0ms (10.8%)

rewrite29.0ms (0.6%)

simplify105.0ms (2.3%)

prune92.0ms (2%)

regimes464.0ms (10.1%)

simplify2.0ms (0%)

end83.0ms (1.8%)

Profiling