Details

analyze368.0ms (7.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.3s (66.2%)

Results

1.6s	2550×	body	1024	valid
686.0ms	1230×	body	2048	valid
536.0ms	1335×	body	512	valid
339.0ms	2412×	body	128	valid
145.0ms	671×	body	256	valid
42.0ms	58×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

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

45.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.3b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.2b	(+.f64 x (hypot.f64 1 x))
✓	2.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite100.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

575×	`log1p-expm1-u_binary64`
575×	`expm1-log1p-u_binary64`
462×	`prod-diff_binary64`
347×	`fma-udef_binary64`
185×	`fma-def_binary64`

Counts

3 → 85

Calls

3 calls:

99.0ms	(hypot.f64 1 x)
99.0ms	(+.f64 x (hypot.f64 1 x))
99.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	120	20
2	1436	20
3	4831	20
4	4804	20
5	4976	20
0	0	0
1	0	0

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-neg_binary64`
722×	`times-frac_binary64`
447×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
340×	`sub-neg_binary64`

Counts

121 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	569
1	305	549
2	805	537
3	2329	537
4	4446	537
5	5590	537

prune74.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	3	150

Error

0.0b

Counts

150 → 3

Alt Table

Status	Error	Program
	45.5b	(log.f64 (/.f64 -1/2 x))
▶	34.3b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
	45.3b	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))

Compiler

Compiled 1967 to 1467 computations (25.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	20.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite53.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

836×	`log1p-expm1-u_binary64`
836×	`expm1-log1p-u_binary64`
103×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Counts

2 → 47

Calls

2 calls:

52.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
52.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	214	23
2	2153	23
3	5050	23
0	0	0
1	0	0

simplify129.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-neg_binary64`
552×	`distribute-rgt-neg-in_binary64`
422×	`distribute-lft-neg-in_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`

Counts

71 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	246
1	42	242
2	88	228
3	223	228
4	500	228
5	1264	228
6	1975	228
7	3745	228
8	4307	228
9	4647	228
10	4957	228
11	4997	228
12	4831	228

prune77.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	56	3	59

Error

Counts

59 → 3

Alt Table

Status	Error	Program
▶	34.3b	(+.f64 (+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5))) x)
	45.5b	(log.f64 (/.f64 -1/2 x))
	45.3b	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))

Compiler

Compiled 929 to 720 computations (22.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5))) x)
✓	0.1b	(*.f64 3/40 (pow.f64 x 5))
✓	0.1b	(*.f64 (pow.f64 x 3) -1/6)
✓	20.9b	(+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5)))

series16.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5)))
4.0ms	(+.f64 (+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5))) x)
3.0ms	(*.f64 3/40 (pow.f64 x 5))
3.0ms	(*.f64 (pow.f64 x 3) -1/6)

rewrite97.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`fma-def_binary64`
315×	`fma-neg_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
162×	`egg-rr`

Counts

4 → 162

Calls

4 calls:

92.0ms	(+.f64 (+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5))) x)
92.0ms	(*.f64 3/40 (pow.f64 x 5))
92.0ms	(*.f64 (pow.f64 x 3) -1/6)
92.0ms	(+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	274	43
2	3258	43
3	4797	43
0	0	0
1	0	0

simplify134.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-neg_binary64`
541×	`distribute-rgt-neg-in_binary64`
418×	`distribute-lft-neg-in_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`

Counts

198 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	408
1	43	386
2	94	372
3	237	372
4	511	372
5	1281	372
6	1983	372
7	3739	372
8	4307	372
9	4647	372
10	4957	372
11	4997	372
12	4831	372

prune106.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	169	3	172

Error

Counts

172 → 3

Alt Table

Status	Error	Program
✓	34.3b	(+.f64 (+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5))) x)
	45.5b	(log.f64 (/.f64 -1/2 x))
▶	45.3b	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))

Compiler

Compiled 3190 to 2462 computations (22.8% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 x)
✓	0.1b	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))
	0.2b	(+.f64 x (hypot.f64 1 x))
✓	2.7b	(-.f64 (+.f64 x (hypot.f64 1 x)) 1)

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))
3.0ms	(-.f64 (+.f64 x (hypot.f64 1 x)) 1)

rewrite52.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

788×	`expm1-log1p-u_binary64`
787×	`log1p-expm1-u_binary64`
639×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`add-cbrt-cube_binary64`

Counts

2 → 64

Calls

2 calls:

50.0ms	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))
50.0ms	(-.f64 (+.f64 x (hypot.f64 1 x)) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	156	19
2	1915	19
3	5971	19
0	0	0
1	0	0

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

514×	`associate-l_binary64`
401×	`cancel-sign-sub-inv_binary64`
401×	`fma-neg_binary64`
394×	`associate-/r*_binary64`
358×	`sub-neg_binary64`

Counts

88 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	385
1	249	375
2	710	367
3	2036	367
4	4503	367
5	4975	367
6	4877	367

prune106.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	214	3	217

Error

Counts

217 → 3

Alt Table

Status	Error	Program
✓	34.3b	(+.f64 (+.f64 (.f64 (pow.f64 x 3) -1/6) (.f64 3/40 (pow.f64 x 5))) x)
	45.5b	(log.f64 (/.f64 -1/2 x))
✓	45.3b	(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))

Compiler

Compiled 3057 to 2362 computations (22.7% saved)

regimes130.0ms (2.6%)

Accuracy

Total 0.3b remaining (74.4%)

Threshold costs 0.3b (74.4%)

Counts

47 → 2

Compiler

Compiled 1350 to 1027 computations (23.9% saved)

bsearch21.0ms (0.4%)

Steps

Iters	Range		Point
10	-15265519445790.742	-5.389217412060972e-5	-8058.760018329849

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	18	25
2	17	25

end58.0ms (1.1%)

Compiler: Compiled 64 to 50 computations (21.9% saved)

Details

analyze368.0ms (7.3%)

sample3.3s (66.2%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite100.0ms (2%)

simplify57.0ms (1.1%)

prune74.0ms (1.5%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite53.0ms (1.1%)

simplify129.0ms (2.6%)

prune77.0ms (1.5%)

localize7.0ms (0.1%)

series16.0ms (0.3%)

rewrite97.0ms (1.9%)

simplify134.0ms (2.7%)

prune106.0ms (2.1%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite52.0ms (1%)

simplify68.0ms (1.3%)

prune106.0ms (2.1%)

regimes130.0ms (2.6%)

bsearch21.0ms (0.4%)

simplify2.0ms (0%)

end58.0ms (1.1%)

Profiling