Details

analyze4.0ms (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 8 to 6 computations (25% saved)

sample825.0ms (38.1%)

Results

799.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.3b	(sqrt.f64 (.f64 2 (.f64 x x)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite4.0ms (0.2%)

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 2 (*.f64 x x)))

simplify94.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1178×	`fma-def_binary64`
437×	`sqr-pow_binary64`
362×	`unswap-sqr_binary64`
342×	`distribute-rgt-neg-in_binary64`
306×	`distribute-lft-neg-in_binary64`

Counts

26 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	208
1	35	202
2	63	202
3	80	202
4	87	202
5	114	202
6	145	202
7	203	202
8	415	202
9	774	202
10	787	202
11	955	202
12	1220	202
13	1628	202
14	2596	202
15	3178	202
16	4810	202
17	4912	202

prune10.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	3	18

Error

0.2b

Counts

18 → 3

Alt Table

Status	Error	Program
▶	30.4b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 189 to 126 computations (33.3% saved)

localize2.0ms (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)

rewrite6.0ms (0.3%)

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:

5.0ms

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

simplify52.0ms (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

prune51.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	20	5	25
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	21	7	28

Error

0.1b

Counts

28 → 7

Alt Table

Status	Error	Program
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
▶	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	31.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
	30.9b	(.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 379 to 312 computations (17.7% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

series218.0ms (10.1%)

Counts

2 → 24

Calls

2 calls:

215.0ms	(*.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 (0.7%)

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)

simplify82.0ms (3.8%)

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

prune50.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Error

0.1b

Counts

80 → 8

Alt Table

Status	Error	Program
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
▶	30.3b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	31.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
	30.9b	(.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 1456 to 1309 computations (10.1% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series313.0ms (14.5%)

Counts

2 → 24

Calls

2 calls:

310.0ms	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))
3.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
11×	`associate-r_binary64`
10×	`prod-exp_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
5.0ms	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))

simplify72.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

695×	`associate-/l/_binary64`
552×	`unswap-sqr_binary64`
348×	`associate-+l+_binary64`
324×	`sqr-pow_binary64`
317×	`*-commutative_binary64`

Counts

82 → 81

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	90	1079
1	179	940
2	531	768
3	778	767
4	1382	767
5	3260	722
6	4808	722

prune53.0ms (2.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	81	8	89

Error

0.1b

Counts

89 → 8

Alt Table

Status	Error	Program
✓	29.3b	(sqrt.f64 (.f64 2 (.f64 x x)))
	31.1b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
✓	30.3b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	31.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
	30.9b	(.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 1309 to 1162 computations (11.2% saved)

regimes145.0ms (6.7%)

Accuracy

Total 0.3b remaining (68%)

Threshold costs 0.3b (68%)

Counts

25 → 2

Compiler

Compiled 994 to 832 computations (16.3% saved)

bsearch17.0ms (0.8%)

Steps

Iters	Range		Point
10	-1.3009389159742584e-299	1.8586031302396505e-299	5.8146655483607e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	25	36
2	33	36
3	38	36
4	40	36
5	40	36

end99.0ms (4.6%)

Compiler: Compiled 135 to 114 computations (15.6% saved)

Details

analyze4.0ms (0.2%)

sample825.0ms (38.1%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite4.0ms (0.2%)

simplify94.0ms (4.3%)

prune10.0ms (0.5%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite6.0ms (0.3%)

simplify52.0ms (2.4%)

prune51.0ms (2.4%)

localize6.0ms (0.3%)

series218.0ms (10.1%)

rewrite15.0ms (0.7%)

simplify82.0ms (3.8%)

prune50.0ms (2.3%)

localize10.0ms (0.4%)

series313.0ms (14.5%)

rewrite14.0ms (0.6%)

simplify72.0ms (3.3%)

prune53.0ms (2.5%)

regimes145.0ms (6.7%)

bsearch17.0ms (0.8%)

simplify6.0ms (0.3%)

end99.0ms (4.6%)

Profiling