Details

analyze96.0ms (1.8%)

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 18 to 14 computations (22.2% saved)

sample89.0ms (1.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify56.0ms (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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize22.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
✓	0.1b	(exp.f32 (/.f32 (neg.f32 x) s))
✓	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

series37.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
8.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
6.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite19.0ms (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:

6.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
4.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
4.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

simplify106.0ms (2%)

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 → 161

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

prune171.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	5	162

Error

0.0b

Counts

162 → 5

Alt Table

Status	Error	Program
▶	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	12.2b	(.f32 (/.f32 1 (+.f32 (pow.f32 1 3) (pow.f32 (exp.f32 (/.f32 (neg.f32 x) s)) 3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.2b	(cbrt.f32 (/.f32 (.f32 (.f32 1 1) 1) (.f32 (.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 2843 to 1523 computations (46.4% saved)

localize27.0ms (0.5%)

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))))))
✓	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	1.5b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series854.0ms (16.4%)

Counts

3 → 64

Calls

3 calls:

490.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
358.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
6.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite10.0ms (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:

3.0ms	(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))))

simplify132.0ms (2.5%)

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 → 118

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

prune115.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Error

0.0b

Counts

123 → 4

Alt Table

Status	Error	Program
	0.3b	(*.f32 (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))) (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
▶	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.2b	(exp.f32 (neg.f32 (log1p.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 x s)) -3)))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))

Compiler

Compiled 1845 to 856 computations (53.6% saved)

localize26.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	1.5b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series678.0ms (13%)

Counts

1 → 24

Calls

1 calls:

678.0ms

(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow-unpow_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`
3×	`distribute-lft-neg-in_binary32`

Counts

1 → 29

Calls

1 calls:

2.0ms

(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

simplify101.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

481×	`associate-/l*_binary32`
463×	`times-frac_binary32`
362×	`fma-def_binary32`
329×	`fma-neg_binary32`
297×	`associate-*l/_binary32`

Counts

53 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	955
1	188	915
2	446	899
3	1429	881
4	4668	881
5	4873	881
6	4998	881
7	4898	881

prune86.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Error

0.0b

Counts

124 → 4

Alt Table

Status	Error	Program
	0.3b	(*.f32 (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))) (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
✓	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.2b	(exp.f32 (neg.f32 (log1p.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 x s)) -3)))))
▶	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))

Compiler

Compiled 1946 to 780 computations (59.9% saved)

localize27.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
✓	0.0b	(pow.f32 (exp.f32 -1) (/.f32 x s))
✓	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))

series41.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
8.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
7.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary32`
22×	`add-sqr-sqrt_binary32`
22×	`add-cube-cbrt_binary32`
21×	`times-frac_binary32`
13×	`pow-unpow_binary32`

Counts

3 → 88

Calls

3 calls:

5.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
4.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
4.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))

simplify106.0ms (2%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary32`
238×	`associate-r_binary32`
236×	`distribute-rgt-neg-in_binary32`
215×	`unswap-sqr_binary32`
212×	`fma-def_binary32`

Counts

160 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2396
1	348	2254
2	869	2200
3	3038	2188
4	4756	2188
5	4929	2188

prune180.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
	0.3b	(*.f32 (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))) (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
✓	0.1b	(pow.f32 (E.f32) (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))))
	0.2b	(exp.f32 (neg.f32 (log1p.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 x s)) -3)))))
	0.3b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))) (cbrt.f32 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))))

Compiler

Compiled 2573 to 1704 computations (33.8% saved)

regimes1.0s (19.5%)

Accuracy

Total 0.0b remaining (53.1%)

Threshold costs 0.0b (53.1%)

Counts

134 → 1

Compiler

Compiled 17414 to 13495 computations (22.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	15	15
2	17	15
3	18	15
4	17	15

end0.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample1.2s (22.8%)

Algorithm

1×

intervals

Results

501.0ms	8000×	body	128	valid
141.0ms	8000×	pre	128	true

Compiler

Compiled 132 to 98 computations (25.8% saved)

Details

analyze96.0ms (1.8%)

sample89.0ms (1.7%)

simplify56.0ms (1.1%)

prune2.0ms (0%)

localize22.0ms (0.4%)

series37.0ms (0.7%)

rewrite19.0ms (0.4%)

simplify106.0ms (2%)

prune171.0ms (3.3%)

localize27.0ms (0.5%)

series854.0ms (16.4%)

rewrite10.0ms (0.2%)

simplify132.0ms (2.5%)

prune115.0ms (2.2%)

localize26.0ms (0.5%)

series678.0ms (13%)

rewrite3.0ms (0.1%)

simplify101.0ms (1.9%)

prune86.0ms (1.6%)

localize27.0ms (0.5%)

series41.0ms (0.8%)

rewrite17.0ms (0.3%)

simplify106.0ms (2%)

prune180.0ms (3.5%)

regimes1.0s (19.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (22.8%)

Profiling