Details

analyze478.0ms (18.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
0%	37.5%	62.5%	4
0%	31.2%	68.8%	5
0%	28.1%	71.9%	6
0%	26.5%	73.5%	7
0%	25.8%	74.2%	8
0%	25.4%	74.6%	9
0%	25.2%	74.8%	10
0%	25.1%	74.9%	11
0%	25%	75%	12
0%	25%	75%	13
0%	25%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.3s (49.9%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify201.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.2b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series21.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
6.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite47.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`distribute-lft-out_binary64`

Counts

3 → 87

Calls

3 calls:

18.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
18.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify91.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
404×	`associate-/r*_binary64`
400×	`associate-l_binary64`
384×	`fma-neg_binary64`
292×	`cancel-sign-sub-inv_binary64`

Counts

123 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	2461
1	535	2286
2	1497	2256
3	4417	2221
4	4906	2221

prune111.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	2	174

Error

Counts

174 → 2

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 3561 to 2483 computations (30.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

series18.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
9.0ms	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64`
4×	`sum-log_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

5.0ms	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
0.0ms	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify131.0ms (5%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
466×	`sub-neg_binary64`
331×	`fma-def_binary64`
222×	`unsub-neg_binary64`
208×	`times-frac_binary64`

Counts

62 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1304
1	374	1227
2	1026	1198
3	3227	1198
4	4677	1198
5	4957	1198
6	4995	1198
7	5000	1198
8	4892	1198

prune83.0ms (3.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	139	2	141

Error

Counts

141 → 2

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 2715 to 1810 computations (33.3% saved)

regimes54.0ms (2.1%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Counts

17 → 1

Compiler

Compiled 589 to 451 computations (23.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	27	16
3	33	16
4	36	16
5	35	16

end47.0ms (1.8%)

Compiler: Compiled 48 to 35 computations (27.1% saved)

Details

analyze478.0ms (18.3%)

sample1.3s (49.9%)

simplify201.0ms (7.7%)

prune2.0ms (0.1%)

localize9.0ms (0.4%)

series21.0ms (0.8%)

rewrite47.0ms (1.8%)

simplify91.0ms (3.5%)

prune111.0ms (4.2%)

localize9.0ms (0.3%)

series18.0ms (0.7%)

rewrite7.0ms (0.3%)

simplify131.0ms (5%)

prune83.0ms (3.2%)

regimes54.0ms (2.1%)

simplify3.0ms (0.1%)

end47.0ms (1.8%)

Profiling