Details

analyze10.0ms (0.4%)

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)

sample25.0ms (1.1%)

Algorithm

1×

intervals

Results

7.0ms

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-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms (0.1%)

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

31.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.3b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`

Counts

1 → 14

Calls

1 calls:

3.0ms

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

simplify156.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
575×	`cube-prod_binary64`
527×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

26 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	211
1	36	205
2	63	205
3	79	205
4	87	205
5	114	205
6	145	205
7	203	205
8	414	205
9	768	205
10	776	205
11	906	205
12	1060	205
13	1223	205
14	1451	205
15	1752	205
16	2100	205
17	2575	205
18	3193	205
19	3389	205
20	3563	205
21	3677	205
22	3724	205
23	3776	205
24	4654	205
25	4739	205
26	4663	205

prune16.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	5	23

Error

0.2b

Counts

23 → 5

Alt Table

Status	Error	Program
✓	31.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.0b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
▶	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.3b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 302 to 227 computations (24.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) x)

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 24

Calls

1 calls:

4.0ms

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

simplify56.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

444×	`cube-div_binary64`
431×	`log-div_binary64`
332×	`associate-l_binary64`
303×	`log-prod_binary64`
288×	`unswap-sqr_binary64`

Counts

24 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	226
1	67	214
2	159	214
3	214	214
4	293	214
5	479	214
6	964	214
7	2475	214
8	3811	214
9	4892	214

prune23.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	22	8	30

Error

0.1b

Counts

30 → 8

Alt Table

Status	Error	Program
✓	31.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.0b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	32.3b	(*.f64 (sqrt.f64 2) x)
	31.1b	(neg.f64 (.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	30.6b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
▶	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	31.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))

Compiler

Compiled 436 to 359 computations (17.7% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

series255.0ms (11.1%)

Counts

2 → 24

Calls

2 calls:

251.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 52

Calls

2 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
4.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)

simplify84.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

501×	`associate-/l/_binary64`
437×	`associate-/r/_binary64`
384×	`*-commutative_binary64`
354×	`fma-def_binary64`
320×	`distribute-rgt-in_binary64`

Counts

76 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	71	778
1	139	669
2	456	669
3	785	669
4	1500	660
5	2968	660
6	4812	660
7	4839	660

prune55.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Error

0.1b

Counts

81 → 9

Alt Table

Status	Error	Program
	31.1b	(neg.f64 (.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
▶	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))))
✓	31.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.0b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	32.3b	(*.f64 (sqrt.f64 2) x)
	30.6b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
✓	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	31.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))

Compiler

Compiled 1590 to 1433 computations (9.9% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))

series478.0ms (20.8%)

Counts

3 → 36

Calls

3 calls:

243.0ms

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

229.0ms

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

6.0ms

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

rewrite45.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
58×	`pow1_binary64`
40×	`cbrt-unprod_binary64`
40×	`prod-exp_binary64`
40×	`pow-prod-down_binary64`

Counts

3 → 98

Calls

3 calls:

20.0ms

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

10.0ms

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

5.0ms

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

simplify230.0ms (10%)

Algorithm

1×	egg-herbie

Rules

619×	`unswap-sqr_binary64`
594×	`fma-def_binary64`
455×	`*-commutative_binary64`
396×	`sqr-pow_binary64`
302×	`log-prod_binary64`

Counts

134 → 126

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	2399
1	244	1293
2	896	1288
3	1801	1279
4	3902	1264
5	4839	1264
6	4872	1264

prune144.0ms (6.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	127	8	135

Error

0.1b

Counts

135 → 8

Alt Table

Status	Error	Program
	31.1b	(neg.f64 (.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))))
✓	31.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.0b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	32.3b	(*.f64 (sqrt.f64 2) x)
✓	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	30.5b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) 8) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)))

Compiler

Compiled 4008 to 3772 computations (5.9% saved)

regimes116.0ms (5%)

Accuracy

Total 0.3b remaining (83.3%)

Threshold costs 0.3b (83.3%)

Counts

26 → 2

Compiler

Compiled 1205 to 1007 computations (16.4% saved)

bsearch12.0ms (0.5%)

Steps

Iters	Range		Point
9	-5.161943190768628e-306	8.376235680206229e-306	-2.2683928527416e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	31	41
2	45	41
3	54	41
4	60	41
5	62	41
6	62	41

end1.0ms (0%)

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

sample533.0ms (23.1%)

Algorithm

1×

intervals

Results

225.0ms

8000×

body

128

valid

Compiler

Compiled 140 to 117 computations (16.4% saved)

Details

analyze10.0ms (0.4%)

sample25.0ms (1.1%)

simplify8.0ms (0.4%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify156.0ms (6.8%)

prune16.0ms (0.7%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite4.0ms (0.2%)

simplify56.0ms (2.4%)

prune23.0ms (1%)

localize6.0ms (0.3%)

series255.0ms (11.1%)

rewrite15.0ms (0.6%)

simplify84.0ms (3.6%)

prune55.0ms (2.4%)

localize9.0ms (0.4%)

series478.0ms (20.8%)

rewrite45.0ms (1.9%)

simplify230.0ms (10%)

prune144.0ms (6.3%)

regimes116.0ms (5%)

bsearch12.0ms (0.5%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample533.0ms (23.1%)

Profiling