Details

analyze159.0ms (3.2%)

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)

sample36.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

863×	`exp-prod_binary32`
518×	`unswap-sqr_binary32`
383×	`div-exp_binary32`
340×	`times-frac_binary32`
333×	`associate-l_binary32`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	27	14
3	36	14
4	48	14
5	71	14
6	136	14
7	247	14
8	504	14
9	1622	14
10	3013	14
11	4342	14
12	4899	14
13	4958	14
14	5253	14

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

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

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize27.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
0.0b	(exp.f32 (/.f32 (neg.f32 x) s))
0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

rewrite127.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 93

Calls

3 calls:

7.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
6.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

Compiler

Compiled 1477 to 748 computations (49.4% saved)

series89.0ms (1.8%)

Error

0.0b

Counts

3 → 42

Calls

3 calls:

31.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
24.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
23.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

Compiler

Compiled 945 to 761 computations (19.5% saved)

simplify135.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

640×	`cancel-sign-sub-inv_binary32`
400×	`sub-neg_binary32`
303×	`associate-/l/_binary32`
253×	`associate-/r/_binary32`
228×	`neg-mul-1_binary32`

Counts

135 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	156	2047
1	315	1948
2	707	1915
3	2075	1879
4	4179	1877
5	4708	1877
6	5069	1877

prune66.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Error

Counts

89 → 3

Alt Table

Status	Error	Program
▶	0.0b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	23.6b	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))
	0.4b	(/.f32 (/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))) (cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 922 to 522 computations (43.4% saved)

localize40.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
0.0b	(*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))
0.1b	(pow.f32 (exp.f32 (/.f32 x s)) -1/2)
0.1b	(pow.f32 (exp.f32 (/.f32 x s)) -1/2)

rewrite216.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

50×	`add-sqr-sqrt_binary32`
38×	`*-un-lft-identity_binary32`
38×	`add-cube-cbrt_binary32`
28×	`pow-pow_binary32`
27×	`times-frac_binary32`

Counts

4 → 145

Calls

4 calls:

9.0ms	(*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))
4.0ms	(pow.f32 (exp.f32 (/.f32 x s)) -1/2)
4.0ms	(pow.f32 (exp.f32 (/.f32 x s)) -1/2)
4.0ms	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))

Compiler

Compiled 3772 to 2049 computations (45.7% saved)

series174.0ms (3.5%)

Error

Counts

4 → 57

Calls

4 calls:

40.0ms	(pow.f32 (exp.f32 (/.f32 x s)) -1/2)
40.0ms	(pow.f32 (exp.f32 (/.f32 x s)) -1/2)
40.0ms	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
28.0ms	(*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))

Compiler

Compiled 1735 to 1322 computations (23.8% saved)

simplify188.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

499×	`cancel-sign-sub-inv_binary32`
433×	`unswap-sqr_binary32`
219×	`log-prod_binary32`
214×	`distribute-rgt-neg-in_binary32`
201×	`distribute-lft-neg-in_binary32`

Counts

202 → 154

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	178	3276
1	357	3014
2	911	2914
3	2264	2811
4	4534	2763
5	4892	2763
6	4899	2763

prune107.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	23.6b	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))
▶	0.4b	(/.f32 (/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))) (cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 1844 to 990 computations (46.3% saved)

localize68.0ms (1.4%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
0.1b	(cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
0.1b	(cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
0.2b	(*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))

rewrite166.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`cbrt-prod_binary32`
35×	`*-un-lft-identity_binary32`
23×	`add-sqr-sqrt_binary32`
18×	`cbrt-div_binary32`
15×	`add-cube-cbrt_binary32`

Counts

4 → 95

Calls

4 calls:

13.0ms	(*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))
5.0ms	(cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
4.0ms	(cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
4.0ms	(cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))

Compiler

Compiled 3385 to 1635 computations (51.7% saved)

series305.0ms (6.1%)

Error

Counts

4 → 60

Calls

4 calls:

72.0ms	(*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))
72.0ms	(cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
64.0ms	(cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
58.0ms	(cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 3485 to 2645 computations (24.1% saved)

simplify122.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

590×	`unswap-sqr_binary32`
561×	`cancel-sign-sub-inv_binary32`
341×	`distribute-neg-frac_binary32`
239×	`*-commutative_binary32`
198×	`times-frac_binary32`

Counts

155 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	4141
1	286	3644
2	892	3422
3	2754	3397
4	5011	3397

prune102.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
▶	23.6b	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))
✓	0.4b	(/.f32 (/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))) (cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 2284 to 1193 computations (47.8% saved)

localize36.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(*.f32 1/4 (/.f32 x s))
0.2b	(pow.f32 (/.f32 x s) 3)
0.7b	(*.f32 1/48 (pow.f32 (/.f32 x s) 3))
6.2b	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))

rewrite161.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`add-sqr-sqrt_binary32`
48×	`times-frac_binary32`
45×	`associate-r_binary32`
43×	`*-un-lft-identity_binary32`
43×	`add-cube-cbrt_binary32`

Counts

4 → 149

Calls

4 calls:

10.0ms	(*.f32 1/48 (pow.f32 (/.f32 x s) 3))
6.0ms	(*.f32 1/4 (/.f32 x s))
5.0ms	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))
4.0ms	(pow.f32 (/.f32 x s) 3)

Compiler

Compiled 2748 to 1632 computations (40.6% saved)

series130.0ms (2.6%)

Error

Counts

4 → 36

Calls

4 calls:

56.0ms	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))
28.0ms	(*.f32 1/48 (pow.f32 (/.f32 x s) 3))
24.0ms	(pow.f32 (/.f32 x s) 3)
17.0ms	(*.f32 1/4 (/.f32 x s))

Compiler

Compiled 1074 to 826 computations (23.1% saved)

simplify141.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

378×	`unswap-sqr_binary32`
360×	`log-prod_binary32`
260×	`cancel-sign-sub-inv_binary32`
241×	`distribute-rgt-neg-in_binary32`
213×	`associate-r_binary32`

Counts

185 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2671
1	558	2456
2	2322	2416
3	4352	2416
4	4995	2416
5	4943	2416

prune55.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	124	3	127

Error

Counts

127 → 3

Alt Table

Status	Error	Program
	0.0b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (exp.f32 (/.f32 x s)) -1/2) (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	23.6b	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (pow.f32 (/.f32 x s) 3)))
	0.4b	(/.f32 (/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))))) (cbrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 1238 to 737 computations (40.5% saved)

regimes895.0ms (17.8%)

Accuracy

Total 0.0b remaining (48.4%)

Threshold costs 0.0b (48.4%)

Compiler

Compiled 10800 to 8220 computations (23.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	11	17
1	21	17
2	27	17
3	31	17
4	32	17
5	31	17

end1.0ms (0%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

sample1.4s (27.5%)

Algorithm

1×

intervals

Results

580.0ms	8000×	body	128	valid
132.0ms	8000×	pre	128	true

Compiler

Compiled 95 to 70 computations (26.3% saved)

Details

analyze159.0ms (3.2%)

sample36.0ms (0.7%)

simplify97.0ms (1.9%)

prune2.0ms (0%)

localize27.0ms (0.5%)

rewrite127.0ms (2.5%)

series89.0ms (1.8%)

simplify135.0ms (2.7%)

prune66.0ms (1.3%)

localize40.0ms (0.8%)

rewrite216.0ms (4.3%)

series174.0ms (3.5%)

simplify188.0ms (3.7%)

prune107.0ms (2.1%)

localize68.0ms (1.4%)

rewrite166.0ms (3.3%)

series305.0ms (6.1%)

simplify122.0ms (2.4%)

prune102.0ms (2%)

localize36.0ms (0.7%)

rewrite161.0ms (3.2%)

series130.0ms (2.6%)

simplify141.0ms (2.8%)

prune55.0ms (1.1%)

regimes895.0ms (17.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.4s (27.5%)

Profiling