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)

sample687.0ms (31.5%)

Results

661.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.3%)

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

prune4.0ms (0.2%)

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

29.3b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.3b	(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 (7.2%)

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

prune15.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	4	23

Error

0.2b

Counts

23 → 4

Alt Table

Status	Error	Program
▶	30.4b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 270 to 203 computations (24.8% 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)

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)

simplify54.0ms (2.5%)

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

prune18.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	23	6	29

Error

0.1b

Counts

29 → 6

Alt Table

Status	Error	Program
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) 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))
	30.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 337 to 280 computations (16.9% saved)

localize5.0ms (0.2%)

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))

series200.0ms (9.2%)

Counts

2 → 24

Calls

2 calls:

197.0ms	(*.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))

rewrite135.0ms (6.2%)

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:

128.0ms	(.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)

simplify81.0ms (3.7%)

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

prune77.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Error

0.1b

Counts

79 → 7

Alt Table

Status	Error	Program
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	30.3b	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.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))
	30.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 1414 to 1277 computations (9.7% saved)

localize7.0ms (0.3%)

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)))

series300.0ms (13.8%)

Counts

2 → 24

Calls

2 calls:

297.0ms	(*.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)))

rewrite15.0ms (0.7%)

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:

7.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))
4.0ms	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))

simplify67.0ms (3.1%)

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 (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	82	6	88

Error

0.1b

Counts

88 → 6

Alt Table

Status	Error	Program
	30.3b	(.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 2))) (.f64 x (pow.f64 (cbrt.f64 (sqrt.f64 2)) 5/2)))
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	30.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1278 to 1138 computations (11% saved)

regimes174.0ms (8%)

Accuracy

Total 0.3b remaining (68.2%)

Threshold costs 0.3b (68.2%)

Counts

33 → 2

Compiler

Compiled 1032 to 884 computations (14.3% 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)

simplify3.0ms (0.1%)

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	15	30
1	26	30
2	34	30
3	39	30
4	41	30
5	41	30

end81.0ms (3.7%)

Compiler: Compiled 98 to 84 computations (14.3% saved)

Details

analyze4.0ms (0.2%)

sample687.0ms (31.5%)

simplify6.0ms (0.3%)

prune4.0ms (0.2%)

localize3.0ms (0.2%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify156.0ms (7.2%)

prune15.0ms (0.7%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite4.0ms (0.2%)

simplify54.0ms (2.5%)

prune18.0ms (0.8%)

localize5.0ms (0.2%)

series200.0ms (9.2%)

rewrite135.0ms (6.2%)

simplify81.0ms (3.7%)

prune77.0ms (3.5%)

localize7.0ms (0.3%)

series300.0ms (13.8%)

rewrite15.0ms (0.7%)

simplify67.0ms (3.1%)

prune53.0ms (2.4%)

regimes174.0ms (8%)

bsearch17.0ms (0.8%)

simplify3.0ms (0.1%)

end81.0ms (3.7%)

Profiling