Details

analyze151.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	24.7%	75.3%	0
0%	24.7%	75.3%	1
0%	24.7%	75.3%	2
12.4%	12.4%	75.3%	3
12.4%	12.4%	75.3%	4
18.5%	6.2%	75.3%	5
18.5%	6.2%	75.3%	6
21.6%	3.1%	75.3%	7
21.6%	3.1%	75.3%	8
23.2%	1.5%	75.3%	9
23.2%	1.5%	75.3%	10
23.9%	0.8%	75.3%	11
23.9%	0.8%	75.3%	12
24.3%	0.4%	75.3%	13
24.3%	0.4%	75.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-neg_binary32`
518×	`unswap-sqr_binary32`
432×	`exp-prod_binary32`
340×	`times-frac_binary32`
333×	`associate-l_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	27	14
3	36	14
4	50	14
5	79	14
6	147	14
7	261	14
8	528	14
9	1676	14
10	3160	14
11	4121	14
12	4850	14

prune2.0ms (0%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize24.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
✓	0.0b	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary32`
42×	`times-frac_binary32`
34×	`exp-prod_binary32`
33×	`add-sqr-sqrt_binary32`
33×	`add-cube-cbrt_binary32`

Counts

3 → 102

Calls

3 calls:

7.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
4.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

series41.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
5.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

simplify126.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary32`
322×	`associate-/l/_binary32`
269×	`associate-/r/_binary32`
197×	`distribute-rgt-neg-in_binary32`
190×	`distribute-lft-neg-in_binary32`

Counts

174 → 301

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2521
1	346	2365
2	806	2311
3	2414	2287
4	4850	2287
5	5089	2287

prune129.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	297	4	301
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	298	4	302

Error

Counts

302 → 4

Alt Table

Status	Error	Program
	0.0b	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
▶	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.0b	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 2704 to 1449 computations (46.4% saved)

localize23.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.0b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	1.6b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`exp-prod_binary32`
21×	`*-un-lft-identity_binary32`
21×	`add-sqr-sqrt_binary32`
21×	`add-cube-cbrt_binary32`
18×	`times-frac_binary32`

Counts

3 → 78

Calls

3 calls:

5.0ms	(exp.f32 (neg.f32 (/.f32 x s)))
2.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
0.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series896.0ms (17%)

Counts

3 → 64

Calls

3 calls:

455.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
435.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
5.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

simplify148.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

452×	`fma-neg_binary32`
354×	`distribute-neg-frac_binary32`
292×	`times-frac_binary32`
241×	`associate-/l*_binary32`
200×	`associate-/r*_binary32`

Counts

142 → 229

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	2142
1	367	1839
2	964	1802
3	3283	1774
4	4792	1772
5	4934	1772
6	4991	1772
7	4918	1772

prune161.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	229	4	233

Error

Counts

233 → 4

Alt Table

Status	Error	Program
▶	0.0b	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.0b	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 1808 to 853 computations (52.8% saved)

localize23.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s))))
✓	0.0b	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
	0.0b	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary32`
30×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
15×	`times-frac_binary32`
9×	`prod-diff_binary32`

Counts

2 → 69

Calls

2 calls:

6.0ms	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
5.0ms	(-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s))))

series38.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
6.0ms	(-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s))))

simplify162.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1107×	`fma-neg_binary32`
346×	`div-sub_binary32`
281×	`associate-l_binary32`
242×	`fma-def_binary32`
224×	`associate-r_binary32`

Counts

117 → 198

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	2296
1	301	2069
2	900	1928
3	3182	1920
4	4169	1911
5	4827	1911
6	4979	1911
7	4825	1911

prune123.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	284	4	288

Error

Counts

288 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
▶	0.0b	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 3166 to 1569 computations (50.4% saved)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))
✓	0.0b	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.0b	(exp.f32 (/.f32 (neg.f32 x) s))
✓	1.6b	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary32`
12×	`times-frac_binary32`
12×	`add-sqr-sqrt_binary32`
12×	`add-cube-cbrt_binary32`
7×	`add-exp-log_binary32`

Counts

3 → 61

Calls

3 calls:

4.0ms	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
0.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))
0.0ms	(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))

series1.3s (25.5%)

Counts

3 → 72

Calls

3 calls:

468.0ms	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
438.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))
437.0ms	(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))

simplify120.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

858×	`fma-neg_binary32`
419×	`times-frac_binary32`
288×	`associate-/l*_binary32`
217×	`associate-/r*_binary32`
195×	`fma-def_binary32`

Counts

133 → 254

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	2224
1	307	2007
2	880	1914
3	3793	1898
4	4928	1898
5	5070	1898

prune150.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	365	4	369

Error

Counts

369 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 -1 (-.f32 -1 (exp.f32 (neg.f32 (/.f32 x s)))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.0b	(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 3304 to 1780 computations (46.1% saved)

regimes358.0ms (6.8%)

Accuracy

Total 0.0b remaining (36.5%)

Threshold costs 0.0b (36.5%)

Compiler

Compiled 5534 to 4519 computations (18.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
3×	`*-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	23	14
3	27	14
4	28	14
5	28	14

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.1s (20.2%)

Algorithm

1×

intervals

Results

432.0ms	8000×	body	128	valid
132.0ms	8000×	pre	128	true

Compiler

Compiled 95 to 72 computations (24.2% saved)

Details

analyze151.0ms (2.9%)

sample38.0ms (0.7%)

simplify60.0ms (1.1%)

prune2.0ms (0%)

localize24.0ms (0.4%)

rewrite22.0ms (0.4%)

series41.0ms (0.8%)

simplify126.0ms (2.4%)

prune129.0ms (2.4%)

localize23.0ms (0.4%)

rewrite11.0ms (0.2%)

series896.0ms (17%)

simplify148.0ms (2.8%)

prune161.0ms (3.1%)

localize23.0ms (0.4%)

rewrite15.0ms (0.3%)

series38.0ms (0.7%)

simplify162.0ms (3.1%)

prune123.0ms (2.3%)

localize30.0ms (0.6%)

rewrite8.0ms (0.1%)

series1.3s (25.5%)

simplify120.0ms (2.3%)

prune150.0ms (2.8%)

regimes358.0ms (6.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (20.2%)

Profiling