Details

analyze365.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	189×	body	128	valid
5.0ms	24×	body	2048	valid
4.0ms	17×	body	4096	valid
3.0ms	256×	pre	128	true
2.0ms	14×	body	1024	valid
1.0ms	9×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify27.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`
27×	`unsub-neg_binary64`
27×	`neg-mul-1_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

prune2.0ms (0%)

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

38.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	38.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite123.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

37.8b

Rules

11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
8×	`pow1_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1329 to 472 computations (64.5% saved)

series160.0ms (3%)

Error

0.6b

Counts

4 → 57

Calls

4 calls:

35.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
34.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
33.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
25.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2106 to 1727 computations (18% saved)

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

645×	`associate-r_binary64`
603×	`associate-l_binary64`
350×	`times-frac_binary64`
267×	`associate-/l*_binary64`
177×	`cancel-sign-sub-inv_binary64`

Counts

113 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2013
1	448	1934
2	1227	1910
3	5111	1910

prune53.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Error

9.4b

Counts

68 → 8

Alt Table

Status	Error	Program
	40.5b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (*.f64 im im)) re))))
	47.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	41.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (+.f64 (.f64 im im) 0) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	53.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (sqrt.f64 (+.f64 (pow.f64 re 6) (pow.f64 im 6))) (sqrt.f64 (+.f64 (pow.f64 re 4) (-.f64 (pow.f64 im 4) (.f64 (.f64 re re) (*.f64 im im)))))) re))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
▶	34.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
✓	38.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 1163 to 721 computations (38% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
0.0b	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
7.2b	(/.f64 (*.f64 re re) im)
9.5b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))

rewrite93.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

6.8b

Rules

11×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 63

Calls

4 calls:

7.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
7.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
5.0ms	(/.f64 (*.f64 re re) im)
4.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))

Compiler

Compiled 1546 to 853 computations (44.8% saved)

series127.0ms (2.4%)

Error

6.9b

Counts

4 → 46

Calls

4 calls:

37.0ms	(-.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re)
32.0ms	(sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (/.f64 (*.f64 re re) im))) re)))
28.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
17.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 1482 to 1205 computations (18.7% saved)

simplify110.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

394×	`associate-*l/_binary64`
392×	`associate-/l*_binary64`
377×	`times-frac_binary64`
363×	`associate-*r/_binary64`
289×	`distribute-rgt-in_binary64`

Counts

109 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	1846
1	380	1744
2	1197	1720
3	4688	1720
4	4991	1720
5	4967	1720

prune48.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	71	8	79

Error

6.7b

Counts

79 → 8

Alt Table

Status	Error	Program
	40.5b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (*.f64 im im)) re))))
	47.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	41.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (+.f64 (.f64 im im) 0) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	31.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
✓	38.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	31.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))

Compiler

Compiled 1178 to 749 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Rules

15×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 31

Calls

1 calls:

7.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 im))

Compiler

Compiled 294 to 220 computations (25.2% saved)

series8.0ms (0.1%)

Error

6.7b

Counts

1 → 3

Calls

1 calls:

7.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 im))

Compiler

Compiled 81 to 73 computations (9.9% saved)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

564×	`log-div_binary64`
359×	`associate-l_binary64`
346×	`log-prod_binary64`
296×	`associate-*l/_binary64`
288×	`unswap-sqr_binary64`

Counts

34 → 13

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	367
1	83	361
2	199	361
3	249	361
4	342	361
5	528	361
6	1013	361
7	2695	361
8	4284	361
9	4989	361
10	4907	361

prune22.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	12	9	21

Error

6.7b

Counts

21 → 9

Alt Table

Status	Error	Program
	40.5b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (*.f64 im im)) re))))
	47.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	41.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (+.f64 (.f64 im im) 0) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
▶	31.6b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	31.8b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) (fabs.f64 (cbrt.f64 im))) (sqrt.f64 (cbrt.f64 im))))
	31.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
✓	38.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 382 to 296 computations (22.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2))))

rewrite85.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Rules

38×	`add-sqr-sqrt_binary64`
35×	`sqrt-prod_binary64`
16×	`rem-sqrt-square_binary64`
15×	`associate-l_binary64`
14×	`pow1_binary64`

Counts

2 → 68

Calls

2 calls:

12.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2))))
9.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 904 to 762 computations (15.7% saved)

series16.0ms (0.3%)

Error

6.7b

Counts

2 → 6

Calls

2 calls:

8.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 im) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 193 to 177 computations (8.3% saved)

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

427×	`cube-div_binary64`
421×	`log-div_binary64`
357×	`associate-l_binary64`
346×	`associate-*l/_binary64`
302×	`log-prod_binary64`

Counts

74 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	1131
1	140	902
2	369	881
3	638	881
4	723	881
5	943	881
6	2299	881
7	3776	881
8	4960	881

prune43.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	52	11	63

Error

6.7b

Counts

63 → 11

Alt Table

Status	Error	Program
	40.5b	(.f64 1/2 (/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 im im) 2) 0)) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))))
	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (*.f64 im im)) re))))
	47.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re -2))))
	41.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (+.f64 (.f64 im im) 0) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))
	31.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))) re))))
	38.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	32.1b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))) (cbrt.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)))) (cbrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))))
	40.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)) 3))))
	33.7b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (exp.f64 (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))))
	32.4b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)) (cbrt.f64 (sqrt.f64 (sqrt.f64 2))))))

Compiler

Compiled 706 to 575 computations (18.6% saved)

regimes2.2s (41.3%)

Accuracy

Total 6.9b remaining (50.3%)

Threshold costs 0b (0%)

Compiler

Compiled 17713 to 13013 computations (26.5% saved)

bsearch115.0ms (2.2%)

Steps

Iters	Range		Point
9	9.52521880153929e+31	1.2060391675599176e+37	2.588079697153549e+33
8	71096.26820711743	211134440.3410705	86846314.06309874
7	3.1279141775377004e-31	9.061624215118433e-30	5.235325772799965e-30
9	-9.5207092731185e-117	-1.9288370316928576e-122	-1.9511813760720313e-122
10	-6.89443641370727e+165	-2.6008541141315942e+151	-2.6442239073885936e+151

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
7×	`+-commutative_binary64`
4×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	137
1	88	137
2	94	137
3	96	137
4	97	137
5	96	137

end3.0ms (0.1%)

Compiler: Compiled 92 to 68 computations (26.1% saved)

sample1.4s (25.6%)

Algorithm

1×

intervals

Results

276.0ms	6051×	body	128	valid
153.0ms	650×	body	2048	valid
141.0ms	523×	body	4096	valid
94.0ms	8000×	pre	128	true
69.0ms	411×	body	1024	valid
35.0ms	250×	body	512	valid
10.0ms	115×	body	256	valid

Compiler

Compiled 322 to 251 computations (22% saved)

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23

Details

analyze365.0ms (6.8%)

sample39.0ms (0.7%)

simplify27.0ms (0.5%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite123.0ms (2.3%)

series160.0ms (3%)

simplify67.0ms (1.2%)

prune53.0ms (1%)

localize13.0ms (0.2%)

rewrite93.0ms (1.7%)

series127.0ms (2.4%)

simplify110.0ms (2.1%)

prune48.0ms (0.9%)

localize5.0ms (0.1%)

rewrite31.0ms (0.6%)

series8.0ms (0.1%)

simplify93.0ms (1.7%)

prune22.0ms (0.4%)

localize7.0ms (0.1%)

rewrite85.0ms (1.6%)

series16.0ms (0.3%)

simplify103.0ms (1.9%)

prune43.0ms (0.8%)

regimes2.2s (41.3%)

bsearch115.0ms (2.2%)

simplify7.0ms (0.1%)

end3.0ms (0.1%)

sample1.4s (25.6%)

Profiling

Iter	Nodes	Cost
0	13	23
1	18	23
2	29	23
3	43	23
4	57	23
5	82	23
6	122	23
7	163	23
8	190	23
9	216	23
10	229	23
11	231	23
12	242	23
13	255	23
14	267	23
15	288	23
16	285	23
17	286	23
18	249	23