Details

analyze332.0ms (9.9%)

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample201.0ms (6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 34 to 20 computations (41.2% saved)

simplify71.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series145.0ms (4.3%)

Counts

2 → 60

Calls

2 calls:

126.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
19.0ms	(/.f64 v (+.f64 t1 u))

rewrite41.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify238.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
383×	`fma-def_binary64`
336×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
286×	`distribute-rgt-in_binary64`

Counts

246 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7288
1	848	7129
2	2435	7053
3	4601	7053
4	5003	7053

prune125.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	216	5	221

Error

0.2b

Counts

221 → 5

Alt Table

Status	Error	Program
	17.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	34.0b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
▶	3.1b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	31.9b	(-.f64 (.f64 2 (.f64 (/.f64 u t1) (/.f64 v t1))) (/.f64 v t1))

Compiler

Compiled 5473 to 2028 computations (62.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1))
✓	3.0b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))

series106.0ms (3.1%)

Counts

2 → 60

Calls

2 calls:

99.0ms	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
7.0ms	(fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
12×	`distribute-lft-neg-in_binary64`

Counts

2 → 69

Calls

2 calls:

3.0ms	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
0.0ms	(fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1))

simplify101.0ms (3%)

Algorithm

1×	egg-herbie

Rules

855×	`times-frac_binary64`
573×	`associate-/l*_binary64`
435×	`associate-/r*_binary64`
285×	`fma-neg_binary64`
239×	`associate-/r/_binary64`

Counts

129 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	3276
1	348	3056
2	1153	2932
3	4910	2932
4	5078	2932

prune99.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Error

0.2b

Counts

151 → 5

Alt Table

Status	Error	Program
	17.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	34.0b	(*.f64 (sqrt.f64 v) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	3.1b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
▶	3.3b	(/.f64 -1 (/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v))

Compiler

Compiled 3245 to 1424 computations (56.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 u (+.f64 (/.f64 u t1) 2) t1)
✓	0.5b	(/.f64 -1 (/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v))
✓	2.9b	(/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v)

series167.0ms (5%)

Counts

3 → 96

Calls

3 calls:

129.0ms	(/.f64 -1 (/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v))
31.0ms	(/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v)
7.0ms	(fma.f64 u (+.f64 (/.f64 u t1) 2) t1)

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

3 → 111

Calls

3 calls:

4.0ms	(/.f64 -1 (/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v))
3.0ms	(/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v)
0.0ms	(fma.f64 u (+.f64 (/.f64 u t1) 2) t1)

simplify146.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

572×	`times-frac_binary64`
539×	`fma-def_binary64`
480×	`associate-/l*_binary64`
405×	`associate-/r/_binary64`
389×	`associate-/r*_binary64`

Counts

207 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	5235
1	501	4773
2	1476	4710
3	4431	4686
4	4985	4686

prune176.0ms (5.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	237	5	242

Error

0.2b

Counts

242 → 5

Alt Table

Status	Error	Program
✓	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	3.1b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
▶	2.9b	(/.f64 -1 (fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v)))
	17.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	3.3b	(/.f64 -1 (/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v))

Compiler

Compiled 5649 to 3033 computations (46.3% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 -1 (fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v)))
✓	2.4b	(fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v))

series201.0ms (6%)

Counts

2 → 72

Calls

2 calls:

169.0ms	(/.f64 -1 (fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v)))
32.0ms	(fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 -1 (fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v)))
0.0ms	(fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v))

simplify89.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

817×	`cancel-sign-sub-inv_binary64`
491×	`fma-neg_binary64`
403×	`times-frac_binary64`
288×	`associate-/l*_binary64`
213×	`associate-/r*_binary64`

Counts

111 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	2881
1	273	2608
2	757	2584
3	3099	2584
4	4991	2584

prune50.0ms (1.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	74	5	79

Error

0.2b

Counts

79 → 5

Alt Table

Status	Error	Program
✓	1.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	3.1b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
✓	2.9b	(/.f64 -1 (fma.f64 (/.f64 u v) (+.f64 2 (/.f64 u t1)) (/.f64 t1 v)))
	17.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	3.3b	(/.f64 -1 (/.f64 (fma.f64 u (+.f64 (/.f64 u t1) 2) t1) v))

Compiler

Compiled 1697 to 807 computations (52.4% saved)

regimes160.0ms (4.7%)

Accuracy

Total 1.1b remaining (84.7%)

Threshold costs 0b (0%)

Counts

46 → 1

Compiler

Compiled 2630 to 1710 computations (35% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end0.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample853.0ms (25.3%)

Algorithm

1×

intervals

Results

426.0ms	8000×	body	128	valid
12.0ms	263×	body	128	invalid

Compiler

Compiled 109 to 68 computations (37.6% saved)

Details

analyze332.0ms (9.9%)

sample201.0ms (6%)

simplify71.0ms (2.1%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series145.0ms (4.3%)

rewrite41.0ms (1.2%)

simplify238.0ms (7.1%)

prune125.0ms (3.7%)

localize8.0ms (0.2%)

series106.0ms (3.1%)

rewrite10.0ms (0.3%)

simplify101.0ms (3%)

prune99.0ms (2.9%)

localize8.0ms (0.2%)

series167.0ms (5%)

rewrite17.0ms (0.5%)

simplify146.0ms (4.3%)

prune176.0ms (5.2%)

localize10.0ms (0.3%)

series201.0ms (6%)

rewrite5.0ms (0.1%)

simplify89.0ms (2.6%)

prune50.0ms (1.5%)

regimes160.0ms (4.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample853.0ms (25.3%)

Profiling