Details

analyze436.0ms (12.8%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample53.0ms (1.6%)

Algorithm

1×

intervals

Results

13.0ms	203×	body	128	valid
5.0ms	15×	body	4096	valid
5.0ms	16×	body	2048	valid
3.0ms	11×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.7b	(+.f64 re (hypot.f64 re im))

series54.0ms (1.6%)

Counts

2 → 32

Calls

2 calls:

43.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
11.0ms	(+.f64 re (hypot.f64 re im))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`

Counts

2 → 32

Calls

2 calls:

4.0ms	(+.f64 re (hypot.f64 re im))
3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
517×	`fma-def_binary64`
437×	`associate-r_binary64`
361×	`associate-l_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

64 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1270
1	435	1196
2	1255	1148
3	4683	1148
4	5413	1148

prune58.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Error

7.2b

Counts

80 → 7

Alt Table

Status	Error	Program
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (.f64 re re) (.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	15.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))

Compiler

Compiled 1886 to 1294 computations (31.4% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))
	0.7b	(+.f64 re (hypot.f64 re im))
✓	4.6b	(exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))

series54.0ms (1.6%)

Counts

2 → 32

Calls

2 calls:

42.0ms	(sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))
11.0ms	(exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`pow1_binary64`
4×	`exp-sum_binary64`
4×	`log-prod_binary64`
4×	`exp-diff_binary64`

Counts

2 → 35

Calls

2 calls:

6.0ms	(sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))
3.0ms	(exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
488×	`fma-def_binary64`
418×	`associate-r_binary64`
337×	`associate-l_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

67 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1360
1	437	1278
2	1249	1230
3	4688	1230
4	5417	1230

prune81.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	144	9	153

Error

7.2b

Counts

153 → 9

Alt Table

Status	Error	Program
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 im)))))
✓	12.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (neg.f64 im))))))
	48.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 re re) (.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))))
▶	16.0b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))

Compiler

Compiled 3335 to 2143 computations (35.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	0.7b	(+.f64 re (hypot.f64 re im))
✓	3.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))
	4.6b	(exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))

series206.0ms (6%)

Counts

2 → 16

Calls

2 calls:

162.0ms	(log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
43.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
0.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
741×	`associate-/r*_binary64`
440×	`cancel-sign-sub-inv_binary64`
146×	`distribute-rgt-in_binary64`
136×	`associate-/r/_binary64`

Counts

38 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	1783
1	561	1493
2	2132	1422
3	5474	1422

prune118.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	176	9	185

Error

7.2b

Counts

185 → 9

Alt Table

Status	Error	Program
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (neg.f64 im))))))
	48.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 re re) (.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	45.5b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 im)))))))
▶	17.2b	(.f64 1/2 (expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))))))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))

Compiler

Compiled 5050 to 3532 computations (30.1% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(+.f64 re (hypot.f64 re im))
✓	1.4b	(exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))))
✓	3.0b	(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))))
	4.6b	(exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))

series202.0ms (5.9%)

Counts

2 → 16

Calls

2 calls:

157.0ms

(exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))))

45.0ms

(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`exp-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`exp-sum_binary64`

Counts

2 → 28

Calls

2 calls:

1.0ms

(exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))))

0.0ms

(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))))

simplify55.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
741×	`associate-/r*_binary64`
440×	`cancel-sign-sub-inv_binary64`
142×	`distribute-rgt-in_binary64`
137×	`*-commutative_binary64`

Counts

44 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	1977
1	580	1617
2	2159	1546
3	5492	1546

prune136.0ms (4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	182	11	193

Error

7.2b

Counts

193 → 11

Alt Table

Status	Error	Program
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	29.6b	(.f64 1/2 (expm1.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))))) (sqrt.f64 (log.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im))))))))))))
	45.5b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 im)))))))
	49.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (neg.f64 im))))))
	50.0b	(.f64 1/2 (expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (neg.f64 im))))))))))
	48.4b	(.f64 1/2 (expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 re re) (.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))))))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	46.0b	(.f64 1/2 (expm1.f64 (exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 im)))))))))
	48.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))

Compiler

Compiled 5508 to 3897 computations (29.2% saved)

regimes360.0ms (10.6%)

Accuracy

Total 2.7b remaining (27.3%)

Threshold costs 0b (0%)

Counts

37 → 2

Compiler

Compiled 4858 to 3684 computations (24.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	37	58
2	37	58

end1.0ms (0%)

Compiler: Compiled 40 to 30 computations (25% saved)

sample1.3s (39.3%)

Algorithm

1×

intervals

Results

386.0ms	6035×	body	128	valid
197.0ms	517×	body	4096	valid
193.0ms	640×	body	2048	valid
107.0ms	432×	body	1024	valid
47.0ms	256×	body	512	valid
17.0ms	120×	body	256	valid

Compiler

Compiled 241 to 189 computations (21.6% saved)

Details

analyze436.0ms (12.8%)

sample53.0ms (1.6%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series54.0ms (1.6%)

rewrite8.0ms (0.2%)

simplify64.0ms (1.9%)

prune58.0ms (1.7%)

localize9.0ms (0.3%)

series54.0ms (1.6%)

rewrite11.0ms (0.3%)

simplify64.0ms (1.9%)

prune81.0ms (2.4%)

localize11.0ms (0.3%)

series206.0ms (6%)

rewrite1.0ms (0%)

simplify51.0ms (1.5%)

prune118.0ms (3.5%)

localize14.0ms (0.4%)

series202.0ms (5.9%)

rewrite4.0ms (0.1%)

simplify55.0ms (1.6%)

prune136.0ms (4%)

regimes360.0ms (10.6%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.3s (39.3%)

Profiling