Details

analyze23.0ms (1%)

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)

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify9.0ms (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

30.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	29.2b	(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))

series13.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

13.0ms

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

simplify182.0ms (8.1%)

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 → 40

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

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	5	41

Error

0.2b

Counts

41 → 5

Alt Table

Status	Error	Program
▶	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

Compiler

Compiled 288 to 217 computations (24.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite5.0ms (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)

series11.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

11.0ms

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

simplify64.0ms (2.9%)

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 → 32

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

prune17.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	28	9	37

Error

0.1b

Counts

37 → 9

Alt Table

Status	Error	Program
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	30.6b	(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))))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.6b	(neg.f64 (.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	30.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

Compiler

Compiled 428 to 354 computations (17.3% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.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))

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))
5.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)

series365.0ms (16.3%)

Counts

2 → 24

Calls

2 calls:

350.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
15.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

simplify96.0ms (4.3%)

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 → 132

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

prune52.0ms (2.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	133	8	141

Error

0.1b

Counts

141 → 8

Alt Table

Status	Error	Program
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
▶	30.1b	(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3))))
	30.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

Compiler

Compiled 1490 to 1352 computations (9.3% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.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)))

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))

series518.0ms (23.1%)

Counts

2 → 24

Calls

2 calls:

506.0ms	(*.f64 x (pow.f64 (sqrt.f64 2) 2/3))
12.0ms	(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3)))

simplify86.0ms (3.8%)

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 → 139

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

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	139	8	147

Error

0.1b

Counts

147 → 8

Alt Table

Status	Error	Program
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
✓	30.1b	(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3))))
	30.1b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

Compiler

Compiled 1374 to 1231 computations (10.4% saved)

regimes79.0ms (3.5%)

Accuracy

Total 0.3b remaining (84%)

Threshold costs 0.3b (84%)

Compiler

Compiled 618 to 503 computations (18.6% saved)

bsearch13.0ms (0.6%)

Steps

Iters	Range		Point
9	-8.914428672144927e-307	2.4518843920107785e-304	7.9778320587535e-311

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (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	39
1	31	39
2	45	39
3	54	39
4	60	39
5	62	39
6	62	39

end2.0ms (0.1%)

Compiler: Compiled 25 to 21 computations (16% saved)

sample565.0ms (25.2%)

Algorithm

1×

intervals

Results

234.0ms

8000×

body

128

valid

Compiler

Compiled 107 to 90 computations (15.9% saved)

Details

analyze23.0ms (1%)

sample13.0ms (0.6%)

simplify9.0ms (0.4%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite3.0ms (0.1%)

series13.0ms (0.6%)

simplify182.0ms (8.1%)

prune15.0ms (0.7%)

localize3.0ms (0.1%)

rewrite5.0ms (0.2%)

series11.0ms (0.5%)

simplify64.0ms (2.9%)

prune17.0ms (0.8%)

localize8.0ms (0.4%)

rewrite15.0ms (0.7%)

series365.0ms (16.3%)

simplify96.0ms (4.3%)

prune52.0ms (2.3%)

localize8.0ms (0.4%)

rewrite14.0ms (0.6%)

series518.0ms (23.1%)

simplify86.0ms (3.8%)

prune53.0ms (2.4%)

regimes79.0ms (3.5%)

bsearch13.0ms (0.6%)

simplify5.0ms (0.2%)

end2.0ms (0.1%)

sample565.0ms (25.2%)

Profiling