Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample2.2s (66.3%)

Results

2.0s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify209.0ms (6.3%)

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)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series16.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite45.0ms (1.3%)

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)))
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify87.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
404×	`associate-/r*_binary64`
399×	`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

prune117.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	171	3	174

Error

Counts

174 → 3

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)))
	1.1b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))))

Compiler

Compiled 3589 to 2507 computations (30.1% 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)))

series15.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
6.0ms	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite7.0ms (0.2%)

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:

4.0ms	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
1.0ms	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify133.0ms (4%)

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

prune92.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	139	3	142

Error

Counts

142 → 3

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)))
▶	1.1b	(exp.f64 (log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))))

Compiler

Compiled 2741 to 1832 computations (33.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.1b	(log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x)))
✓	0.2b	(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))
✓	1.1b	(exp.f64 (log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))))

series25.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

10.0ms

(log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x)))

8.0ms

(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))

7.0ms

(exp.f64 (log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`log-prod_binary64`
12×	`prod-diff_binary64`

Counts

3 → 80

Calls

3 calls:

10.0ms

(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))

3.0ms

(log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x)))

3.0ms

(exp.f64 (log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))))

simplify103.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-def_binary64`
353×	`fma-neg_binary64`
269×	`times-frac_binary64`
236×	`distribute-rgt-in_binary64`
200×	`unswap-sqr_binary64`

Counts

116 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3308
1	584	3021
2	1900	2898
3	4874	2898
4	5002	2898

prune96.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	168	3	171

Error

Counts

171 → 3

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)))
✓	1.1b	(exp.f64 (log.f64 (-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (log.f64 x))))

Compiler

Compiled 4216 to 2882 computations (31.6% saved)

regimes58.0ms (1.7%)

Accuracy

Total 0.2b remaining (99.4%)

Threshold costs 0.2b (99.4%)

Counts

19 → 1

Compiler

Compiled 637 to 493 computations (22.6% saved)

simplify2.0ms (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

end60.0ms (1.8%)

Compiler: Compiled 61 to 45 computations (26.2% saved)

Details

analyze5.0ms (0.2%)

sample2.2s (66.3%)

simplify209.0ms (6.3%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series16.0ms (0.5%)

rewrite45.0ms (1.3%)

simplify87.0ms (2.6%)

prune117.0ms (3.5%)

localize9.0ms (0.3%)

series15.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify133.0ms (4%)

prune92.0ms (2.8%)

localize11.0ms (0.3%)

series25.0ms (0.8%)

rewrite21.0ms (0.6%)

simplify103.0ms (3.1%)

prune96.0ms (2.9%)

regimes58.0ms (1.7%)

simplify2.0ms (0.1%)

end60.0ms (1.8%)

Profiling