Details

analyze21.0ms (1.2%)

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 8 to 6 computations (25% saved)

sample12.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-l_binary64` `associate-r_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune7.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.9b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

29.8b

(sqrt.f64 (*.f64 (*.f64 2 x) x))

rewrite16.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

14.8b

Rules

7×	`pow1_binary64`
3×	`pow-prod-down_binary64` `sqrt-pow1_binary64`
1×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`

Counts

1 → 12

Calls

1 calls:

4.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

Compiler

Compiled 115 to 85 computations (26.1% saved)

series10.0ms (0.6%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

7.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

Compiler

Compiled 45 to 37 computations (17.8% saved)

simplify161.0ms (9%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

15 → 10

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	129
1	34	123
2	61	123
3	77	123
4	85	123
5	106	123
6	127	123
7	185	123
8	396	123
9	700	123
10	702	123
11	832	123
12	986	123
13	1154	123
14	1383	123
15	1684	123
16	2032	123
17	2507	123
18	3125	123
19	3321	123
20	3495	123
21	3609	123
22	3656	123
23	3708	123
24	4586	123
25	4865	123

prune14.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	4	11

Error

0.2b

Counts

11 → 4

Alt Table

Status	Error	Program
	32.3b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
▶	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))
	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 150 to 113 computations (24.7% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))
29.8b	(sqrt.f64 (.f64 x (.f64 x 2)))
29.8b	(sqrt.f64 (.f64 x (.f64 x 2)))

rewrite107.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

158×	`pow1_binary64`
154×	`sqrt-pow1_binary64`
82×	`pow-prod-down_binary64`
33×	`sqrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

4 → 132

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))
4.0ms	(sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))
3.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))
3.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))

Compiler

Compiled 1756 to 1340 computations (23.7% saved)

series38.0ms (2.1%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))
8.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))
8.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))

Compiler

Compiled 394 to 318 computations (19.3% saved)

simplify138.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

596×	`log-div_binary64`
471×	`associate-*l/_binary64`
373×	`associate-*r/_binary64`
332×	`associate-l_binary64`
320×	`*-commutative_binary64`

Counts

144 → 108

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	71	1428
1	109	1326
2	310	1296
3	871	1190
4	1339	1160
5	1792	1160
6	3624	1142
7	4881	1142
8	5306	1142

prune31.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

0.2b

Counts

112 → 4

Alt Table

Status	Error	Program
	32.3b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
✓	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))
▶	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 610 to 468 computations (23.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 x (sqrt.f64 2))

rewrite20.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

(*.f64 x (sqrt.f64 2))

Compiler

Compiled 191 to 157 computations (17.8% saved)

series8.0ms (0.4%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

7.0ms

(*.f64 x (sqrt.f64 2))

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify66.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

507×	`log-div_binary64`
340×	`log-prod_binary64`
331×	`associate-l_binary64`
288×	`unswap-sqr_binary64`
278×	`associate-*l/_binary64`

Counts

25 → 8

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	223
1	68	211
2	166	211
3	208	211
4	292	211
5	480	211
6	966	211
7	2596	211
8	3940	211
9	4921	211

prune8.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	7	1	8
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	7	5	12

Error

0.2b

Counts

12 → 5

Alt Table

Status	Error	Program
	32.3b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
✓	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))
▶	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
✓	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 123 to 90 computations (26.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite63.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1148 to 491 computations (57.2% saved)

series74.0ms (4.1%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

20.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
18.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

Compiler

Compiled 493 to 373 computations (24.3% saved)

simplify92.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

735×	`log-prod_binary64`
577×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
287×	`associate-l_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	624
1	94	576
2	292	556
3	763	542
4	1759	418
5	4280	418
6	4543	418
7	4810	418

prune25.0ms (1.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	62	7	69

Error

0.1b

Counts

69 → 7

Alt Table

Status	Error	Program
	32.3b	(.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x))
	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2)))))
	32.0b	(neg.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 5) (cbrt.f64 (cbrt.f64 x))) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
	30.9b	(sqrt.f64 (.f64 (.f64 2 x) x))
	32.0b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (.f64 (sqrt.f64 2) (cbrt.f64 x))))

Compiler

Compiled 527 to 324 computations (38.5% saved)

regimes325.0ms (18.1%)

Accuracy

Total 0.2b remaining (46.5%)

Threshold costs 0.2b (46.5%)

Compiler

Compiled 3002 to 2026 computations (32.5% saved)

bsearch13.0ms (0.7%)

Steps

Iters	Range		Point
9	-6.9717952857711765e-307	4.207346151756919e-305	1.25277216594145e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `+-commutative_binary64`
1×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	29	41
2	43	41
3	54	41
4	60	41
5	62	41
6	62	41

end1.0ms (0.1%)

Compiler: Compiled 26 to 22 computations (15.4% saved)

sample507.0ms (28.3%)

Algorithm

1×

intervals

Results

192.0ms

8000×

body

128

valid

Compiler

Compiled 122 to 89 computations (27% saved)

Details

analyze21.0ms (1.2%)

sample12.0ms (0.7%)

simplify8.0ms (0.4%)

prune7.0ms (0.4%)

localize4.0ms (0.2%)

rewrite16.0ms (0.9%)

series10.0ms (0.6%)

simplify161.0ms (9%)

prune14.0ms (0.8%)

localize6.0ms (0.4%)

rewrite107.0ms (6%)

series38.0ms (2.1%)

simplify138.0ms (7.7%)

prune31.0ms (1.7%)

localize4.0ms (0.2%)

rewrite20.0ms (1.1%)

series8.0ms (0.4%)

simplify66.0ms (3.7%)

prune8.0ms (0.5%)

localize8.0ms (0.4%)

rewrite63.0ms (3.5%)

series74.0ms (4.1%)

simplify92.0ms (5.1%)

prune25.0ms (1.4%)

regimes325.0ms (18.1%)

bsearch13.0ms (0.7%)

simplify5.0ms (0.3%)

end1.0ms (0.1%)

sample507.0ms (28.3%)

Profiling