Details

analyze394.0ms (16.3%)

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 7 computations (12.5% saved)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify160.0ms (6.6%)

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 → 1

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

prune5.0ms (0.2%)

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 2 (pow.f64 x 2)))

Compiler

Compiled 21 to 17 computations (19% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 2 (pow.f64 x 2))
29.8b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

rewrite66.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64` `unswap-sqr_binary64`

Counts

2 → 37

Calls

2 calls:

6.0ms	(*.f64 2 (pow.f64 x 2))
4.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 421 to 357 computations (15.2% saved)

series30.0ms (1.3%)

Error

0.3b

Counts

2 → 6

Calls

2 calls:

16.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
7.0ms	(*.f64 2 (pow.f64 x 2))

Compiler

Compiled 93 to 78 computations (16.1% saved)

simplify102.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

823×	`unswap-sqr_binary64`
510×	`log-prod_binary64`
427×	`*-commutative_binary64`
375×	`exp-prod_binary64`
358×	`times-frac_binary64`

Counts

43 → 35

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	411
1	106	370
2	241	358
3	819	352
4	1326	352
5	3312	352
6	4029	352
7	4714	352
8	5042	352

prune25.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	30	5	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	6	36

Error

0.2b

Counts

36 → 6

Alt Table

Status	Error	Program
▶	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
	51.0b	(sqrt.f64 (cbrt.f64 (*.f64 8 (pow.f64 x 6))))
	31.7b	(*.f64 (sqrt.f64 2) x)
	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	48.3b	(sqrt.f64 (*.f64 (+.f64 x x) (pow.f64 (sqrt.f64 x) 2)))

Compiler

Compiled 346 to 237 computations (31.5% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite113.0ms (4.7%)

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:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
5.0ms	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 1756 to 1138 computations (35.2% saved)

series38.0ms (1.6%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
8.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
8.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))

Compiler

Compiled 394 to 315 computations (20.1% saved)

simplify136.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

596×	`log-div_binary64`
471×	`associate-*l/_binary64`
383×	`associate-*r/_binary64`
341×	`*-commutative_binary64`
330×	`associate-l_binary64`

Counts

144 → 111

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	70	1383
1	110	1311
2	321	1261
3	904	1145
4	1405	1145
5	1856	1145
6	3703	1127
7	4958	1127
8	5380	1127

prune38.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	111	6	117

Error

0.2b

Counts

117 → 6

Alt Table

Status	Error	Program
✓	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
	31.7b	(*.f64 (sqrt.f64 2) x)
	47.1b	(pow.f64 (*.f64 4 (pow.f64 x 4)) (/.f64 1/2 2))
▶	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	48.3b	(sqrt.f64 (*.f64 (+.f64 x x) (pow.f64 (sqrt.f64 x) 2)))

Compiler

Compiled 683 to 462 computations (32.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite19.0ms (0.8%)

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)

series9.0ms (0.4%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

8.0ms

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

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify67.0ms (2.8%)

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

prune11.0ms (0.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	7	1	8
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	7	7	14

Error

0.2b

Counts

14 → 7

Alt Table

Status	Error	Program
✓	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
▶	31.7b	(*.f64 (sqrt.f64 2) x)
	47.1b	(pow.f64 (*.f64 4 (pow.f64 x 4)) (/.f64 1/2 2))
✓	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	48.3b	(sqrt.f64 (*.f64 (+.f64 x x) (pow.f64 (sqrt.f64 x) 2)))

Compiler

Compiled 157 to 118 computations (24.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_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-r_binary64`
2×	`unswap-sqr_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

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

Compiler

Compiled 173 to 139 computations (19.7% saved)

series8.0ms (0.3%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

7.0ms

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

Compiler

Compiled 35 to 28 computations (20% saved)

simplify67.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

444×	`cube-div_binary64`
431×	`log-div_binary64`
363×	`cube-prod_binary64`
332×	`associate-l_binary64`
303×	`log-prod_binary64`

Counts

25 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	228
1	65	216
2	157	216
3	212	216
4	291	216
5	477	216
6	962	216
7	2473	216
8	3809	216
9	5056	216

prune17.0ms (0.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	13	9	22

Error

0.1b

Counts

22 → 9

Alt Table

Status	Error	Program
	31.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 x x)))))
	31.7b	(*.f64 (sqrt.f64 2) x)
	47.1b	(pow.f64 (*.f64 4 (pow.f64 x 4)) (/.f64 1/2 2))
	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
	30.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
	31.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 x (cbrt.f64 (sqrt.f64 2))))
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	31.6b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 (sqrt.f64 2))))
	32.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))

Compiler

Compiled 204 to 170 computations (16.7% saved)

regimes370.0ms (15.3%)

Accuracy

Total 0.3b remaining (72.6%)

Threshold costs 0.3b (72.6%)

Compiler

Compiled 2834 to 2325 computations (18% saved)

bsearch18.0ms (0.8%)

Steps

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

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.2%)

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	16	45
1	28	45
2	42	45
3	53	45
4	59	45
5	61	45
6	61	45

end2.0ms (0.1%)

Compiler: Compiled 28 to 25 computations (10.7% saved)

sample652.0ms (27%)

Algorithm

1×

intervals

Results

275.0ms

8000×

body

128

valid

Compiler

Compiled 136 to 113 computations (16.9% saved)

Details

analyze394.0ms (16.3%)

sample19.0ms (0.8%)

simplify160.0ms (6.6%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite66.0ms (2.7%)

series30.0ms (1.3%)

simplify102.0ms (4.2%)

prune25.0ms (1%)

localize9.0ms (0.4%)

rewrite113.0ms (4.7%)

series38.0ms (1.6%)

simplify136.0ms (5.6%)

prune38.0ms (1.6%)

localize4.0ms (0.2%)

rewrite19.0ms (0.8%)

series9.0ms (0.4%)

simplify67.0ms (2.8%)

prune11.0ms (0.5%)

localize3.0ms (0.1%)

rewrite20.0ms (0.8%)

series8.0ms (0.3%)

simplify67.0ms (2.8%)

prune17.0ms (0.7%)

regimes370.0ms (15.3%)

bsearch18.0ms (0.8%)

simplify5.0ms (0.2%)

end2.0ms (0.1%)

sample652.0ms (27%)

Profiling