Details

analyze519.0ms (9.4%)

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)

sample2.0s (35.6%)

Results

884.0ms	6280×	body	128	valid
389.0ms	519×	body	4096	valid
351.0ms	663×	body	2048	valid
186.0ms	422×	body	1024	valid
79.0ms	239×	body	512	valid
32.0ms	133×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify29.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

11.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.0b	(hypot.f64 re im)
✓	0.9b	(-.f64 (hypot.f64 re im) re)

series71.0ms (1.3%)

Counts

3 → 56

Calls

3 calls:

45.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
14.0ms	(-.f64 (hypot.f64 re im) re)
11.0ms	(hypot.f64 re im)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
6×	`pow1_binary64`

Counts

3 → 55

Calls

3 calls:

7.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
3.0ms	(-.f64 (hypot.f64 re im) re)
0.0ms	(hypot.f64 re im)

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
747×	`times-frac_binary64`
413×	`cancel-sign-sub-inv_binary64`
173×	`fma-def_binary64`
158×	`sub-neg_binary64`

Counts

111 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	2332
1	611	2069
2	2078	1999
3	4466	1989
4	5015	1989

prune89.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Error

0.1b

Counts

138 → 5

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	54.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))

Compiler

Compiled 3313 to 2168 computations (34.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (hypot.f64 re im))
	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
✓	13.1b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series147.0ms (2.6%)

Counts

3 → 26

Calls

3 calls:

88.0ms

(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

40.0ms

(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

19.0ms

(sqrt.f64 (hypot.f64 re im))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 38

Calls

3 calls:

2.0ms

(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

1.0ms

(sqrt.f64 (hypot.f64 re im))

0.0ms

(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-def_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
291×	`fma-neg_binary64`
289×	`cancel-sign-sub-inv_binary64`

Counts

64 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	1414
1	518	1316
2	1585	1263
3	4927	1261
4	5024	1261

prune129.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	207	5	212

Error

0.1b

Counts

212 → 5

Alt Table

Status	Error	Program
▶	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	54.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))

Compiler

Compiled 5662 to 3301 computations (41.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(*.f64 (sqrt.f64 2) im)
✓	0.5b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

series39.0ms (0.7%)

Counts

4 → 0

Calls

4 calls:

24.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
7.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
5.0ms	(sqrt.f64 (/.f64 1 re))
3.0ms	(*.f64 (sqrt.f64 2) im)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`pow1_binary64`

Counts

4 → 114

Calls

4 calls:

11.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
5.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
4.0ms	(*.f64 (sqrt.f64 2) im)
2.0ms	(sqrt.f64 (/.f64 1 re))

simplify116.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-/l*_binary64`
416×	`*-commutative_binary64`
403×	`unswap-sqr_binary64`
271×	`sqr-pow_binary64`
214×	`associate-l_binary64`

Counts

114 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	121	1600
1	239	1498
2	789	1498
3	1286	1498
4	2620	1498
5	3060	1498
6	4473	1498
7	5012	1498

prune97.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	118	10	128

Error

0.0b

Counts

128 → 10

Alt Table

Status	Error	Program
	49.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 1 re))))))
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im)))) (sqrt.f64 (/.f64 1 re))))
▶	49.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	49.6b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 (sqrt.f64 re)))) (sqrt.f64 (/.f64 1 (sqrt.f64 re)))))
	49.6b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (sqrt.f64 (/.f64 1 (cbrt.f64 re)))))
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 re))) (sqrt.f64 (cbrt.f64 (/.f64 1 re))))))
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	49.7b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 2) (.f64 (cbrt.f64 im) (cbrt.f64 im))) (cbrt.f64 im))) (sqrt.f64 (/.f64 1 re))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 2895 to 2438 computations (15.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 2)) im)
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))
✓	0.5b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)))

series40.0ms (0.7%)

Counts

4 → 36

Calls

4 calls:

25.0ms	(.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))
6.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)))
6.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) im)
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`sqrt-prod_binary64`
34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
34×	`pow1_binary64`
27×	`add-sqr-sqrt_binary64`

Counts

4 → 120

Calls

4 calls:

19.0ms	(.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))
10.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) im)

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

746×	`associate-/l*_binary64`
609×	`*-commutative_binary64`
357×	`associate-/r*_binary64`
331×	`associate-l_binary64`
320×	`unswap-sqr_binary64`

Counts

156 → 166

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	140	2349
1	301	2120
2	1133	2120
3	1939	2120
4	4346	2120
5	5205	2120

prune173.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	5	2	7
Picked	1	0	1
Done	0	2	2
Total	167	9	176

Error

0.0b

Counts

176 → 9

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 (sqrt.f64 re)))) (sqrt.f64 (/.f64 1 (sqrt.f64 re)))))
	49.5b	(.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im)) (sqrt.f64 (/.f64 1 re)))))
	50.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (exp.f64 (log.f64 (*.f64 im (sqrt.f64 (sqrt.f64 2))))))) (sqrt.f64 (/.f64 1 re))))
	49.5b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) im)) (sqrt.f64 (/.f64 1 re))))
	58.3b	(.f64 1/2 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re)))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))))
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 re))) (sqrt.f64 (cbrt.f64 (/.f64 1 re))))))
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	49.6b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 re) (cbrt.f64 re))))) (sqrt.f64 (/.f64 1 (cbrt.f64 re)))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 4403 to 3888 computations (11.7% saved)

regimes1.5s (27.6%)

Accuracy

Total 6.2b remaining (97.2%)

Threshold costs 0b (0%)

Counts

110 → 2

Compiler

Compiled 17524 to 15277 computations (12.8% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	66
1	41	66
2	46	66
3	48	66
4	49	66
5	48	66

end178.0ms (3.2%)

Compiler: Compiled 318 to 263 computations (17.3% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Details

analyze519.0ms (9.4%)

sample2.0s (35.6%)

simplify29.0ms (0.5%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series71.0ms (1.3%)

rewrite13.0ms (0.2%)

simplify92.0ms (1.7%)

prune89.0ms (1.6%)

localize10.0ms (0.2%)

series147.0ms (2.6%)

rewrite4.0ms (0.1%)

simplify72.0ms (1.3%)

prune129.0ms (2.3%)

localize10.0ms (0.2%)

series39.0ms (0.7%)

rewrite28.0ms (0.5%)

simplify116.0ms (2.1%)

prune97.0ms (1.8%)

localize15.0ms (0.3%)

series40.0ms (0.7%)

rewrite51.0ms (0.9%)

simplify100.0ms (1.8%)

prune173.0ms (3.1%)

regimes1.5s (27.6%)

bsearch6.0ms (0.1%)

simplify4.0ms (0.1%)

end178.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15