Details

analyze141.0ms (6.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	8	12
2	8	12

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
28.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

Rules

4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 26

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 436 to 90 computations (79.4% saved)

series61.0ms (2.7%)

Error

0.0b

Counts

2 → 26

Calls

2 calls:

28.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 514 to 393 computations (23.5% saved)

simplify75.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

606×	`cancel-sign-sub-inv_binary64`
499×	`unswap-sqr_binary64`
279×	`associate-r_binary64`
275×	`times-frac_binary64`
258×	`neg-mul-1_binary64`

Counts

52 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	749
1	212	711
2	618	711
3	2663	711
4	4718	711
5	5035	711

prune18.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Error

2.4b

Counts

33 → 4

Alt Table

Status	Error	Program
	33.2b	(-.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) re)
▶	31.4b	(neg.f64 re)
	33.9b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
✓	30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 321 to 161 computations (49.8% saved)

localize1.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 2.4b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune4.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

2.4b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	33.2b	(-.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) re)
✓	31.4b	(neg.f64 re)
	33.9b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
✓	30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (/.f64 (.f64 im im) re) -1/2)
0.0b	(-.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) re)
6.2b	(/.f64 (*.f64 im im) re)

rewrite68.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`times-frac_binary64` `associate-l_binary64`
5×	`pow1_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64`

Counts

3 → 63

Calls

3 calls:

7.0ms	(.f64 (/.f64 (.f64 im im) re) -1/2)
7.0ms	(/.f64 (*.f64 im im) re)
7.0ms	(-.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) re)

Compiler

Compiled 986 to 401 computations (59.3% saved)

series73.0ms (3.2%)

Error

2.4b

Counts

3 → 24

Calls

3 calls:

31.0ms	(-.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) re)
21.0ms	(.f64 (/.f64 (.f64 im im) re) -1/2)
18.0ms	(/.f64 (*.f64 im im) re)

Compiler

Compiled 490 to 361 computations (26.3% saved)

simplify80.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

601×	`times-frac_binary64`
455×	`associate-l_binary64`
427×	`associate-*l/_binary64`
374×	`associate-/l*_binary64`
355×	`associate-r_binary64`

Counts

87 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	1085
1	259	989
2	778	989
3	4341	989
4	4953	989

prune23.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	53	6	59

Error

2.4b

Counts

59 → 6

Alt Table

Status	Error	Program
	31.6b	(-.f64 (.f64 (.f64 im (/.f64 im re)) -1/2) re)
✓	31.4b	(neg.f64 re)
▶	31.6b	(-.f64 (.f64 (/.f64 im (.f64 (cbrt.f64 re) (cbrt.f64 re))) (*.f64 -1/2 (/.f64 im (cbrt.f64 re)))) re)
	33.9b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
	31.6b	(-.f64 (.f64 (/.f64 (.f64 (/.f64 im (*.f64 (cbrt.f64 re) (cbrt.f64 re))) im) (cbrt.f64 re)) -1/2) re)
✓	30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 426 to 204 computations (52.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
0.6b	(cbrt.f64 re)
0.6b	(cbrt.f64 re)
0.6b	(cbrt.f64 re)

rewrite74.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
1.0ms	(cbrt.f64 re)
1.0ms	(cbrt.f64 re)
1.0ms	(cbrt.f64 re)

Compiler

Compiled 1421 to 493 computations (65.3% saved)

series81.0ms (3.5%)

Error

2.4b

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
19.0ms	(cbrt.f64 re)
16.0ms	(cbrt.f64 re)
16.0ms	(cbrt.f64 re)

Compiler

Compiled 646 to 424 computations (34.4% saved)

simplify93.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

735×	`log-prod_binary64`
577×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
287×	`associate-l_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	624
1	94	576
2	292	556
3	763	542
4	1759	418
5	4280	418
6	4543	418
7	4810	418

prune26.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	66	4	70

Error

2.4b

Counts

70 → 4

Alt Table

Status	Error	Program
	31.4b	(neg.f64 re)
	33.9b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
	30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
	31.6b	(-.f64 (.f64 (/.f64 im (.f64 (.f64 (cbrt.f64 (cbrt.f64 re)) (cbrt.f64 (cbrt.f64 re))) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4))) (.f64 -1/2 (/.f64 im (cbrt.f64 re)))) re)

Compiler

Compiled 612 to 296 computations (51.6% saved)

regimes576.0ms (25.3%)

Accuracy

Total 5.3b remaining (72.6%)

Threshold costs 0b (0%)

Compiler

Compiled 4718 to 2699 computations (42.8% saved)

bsearch25.0ms (1.1%)

Steps

Iters	Range		Point
4	1.3535035317635665e+114	2.1111539912077888e+114	2.040124260634893e+114
9	8.083397943484731e-148	1.8298734702594037e-138	1.542344810860402e-147

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	64
1	33	64
2	38	64
3	40	64
4	41	64
5	41	64

end8.0ms (0.3%)

Compiler: Compiled 129 to 72 computations (44.2% saved)

sample762.0ms (33.4%)

Algorithm

1×

intervals

Results

239.0ms

8000×

body

128

valid

Compiler

Compiled 107 to 63 computations (41.1% saved)

Details

analyze141.0ms (6.2%)

sample21.0ms (0.9%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite26.0ms (1.2%)

series61.0ms (2.7%)

simplify75.0ms (3.3%)

prune18.0ms (0.8%)

localize1.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.3%)

prune4.0ms (0.2%)

localize6.0ms (0.2%)

rewrite68.0ms (3%)

series73.0ms (3.2%)

simplify80.0ms (3.5%)

prune23.0ms (1%)

localize10.0ms (0.4%)

rewrite74.0ms (3.2%)

series81.0ms (3.5%)

simplify93.0ms (4.1%)

prune26.0ms (1.2%)

regimes576.0ms (25.3%)

bsearch25.0ms (1.1%)

simplify5.0ms (0.2%)

end8.0ms (0.3%)

sample762.0ms (33.4%)

Profiling