Details

analyze171.0ms (2.7%)

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 35 to 18 computations (48.6% saved)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 65 to 33 computations (49.2% saved)

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary32`
440×	`times-frac_binary32`
349×	`distribute-rgt-in_binary32`
300×	`fma-neg_binary32`
273×	`distribute-rgt-out_binary32`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	38	43
2	82	41
3	181	41
4	357	39
5	772	30
6	2292	29
7	3341	29
8	4243	29
9	4922	29
10	4875	29

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
▶	0.1b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

Status

Error

Program

0.1b

(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))

▶

0.1b

(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

Compiler

Compiled 142 to 75 computations (47.2% saved)

localize49.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)
✓	0.0b	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
✓	0.0b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.0b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

series108.0ms (1.7%)

Counts

4 → 80

Calls

4 calls:

73.0ms	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
13.0ms	(+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)
13.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
10.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))

rewrite68.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

194×	`times-frac_binary32`
181×	`*-un-lft-identity_binary32`
118×	`add-sqr-sqrt_binary32`
109×	`add-cube-cbrt_binary32`
83×	`exp-prod_binary32`

Counts

4 → 226

Calls

4 calls:

21.0ms	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
10.0ms	(+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)
7.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
4.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))

simplify251.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

512×	`times-frac_binary32`
341×	`associate-/l*_binary32`
335×	`associate-/r*_binary32`
292×	`distribute-rgt-in_binary32`
268×	`distribute-lft-in_binary32`

Counts

306 → 305

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	7856
1	653	7564
2	1636	7474
3	4591	7474
4	4965	7474
5	4914	7474

prune417.0ms (6.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	301	4	305
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	303	4	307

Error

0.0b

Counts

307 → 4

Alt Table

Status	Error	Program
	0.8b	(exp.f32 (-.f32 (neg.f32 (log.f32 s)) (log.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))))
▶	0.1b	(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
	0.1b	(*.f32 (/.f32 1 (sqrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))))))) (/.f32 (/.f32 1 s) (sqrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))))))))
	0.1b	(/.f32 1 (fma.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) s (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))

Compiler

Compiled 9163 to 3605 computations (60.7% saved)

localize54.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
✓	0.0b	(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
✓	0.1b	(exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s)))
✓	8.7b	(sqrt.f32 (/.f32 (fabs.f32 x) s))

series580.0ms (9%)

Counts

3 → 18

Calls

3 calls:

534.0ms

(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

27.0ms

(exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s)))

19.0ms

(sqrt.f32 (/.f32 (fabs.f32 x) s))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`times-frac_binary32`
158×	`*-un-lft-identity_binary32`
101×	`add-sqr-sqrt_binary32`
88×	`add-cube-cbrt_binary32`
50×	`sqrt-prod_binary32`

Counts

3 → 183

Calls

3 calls:

19.0ms

(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

5.0ms

(exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s)))

3.0ms

(sqrt.f32 (/.f32 (fabs.f32 x) s))

simplify176.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-+l+_binary32`
527×	`associate-/l*_binary32`
329×	`associate-*r/_binary32`
258×	`associate-/r/_binary32`
245×	`distribute-rgt-in_binary32`

Counts

201 → 215

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	7949
1	432	6063
2	939	5987
3	2556	5982
4	5321	5982

prune441.0ms (6.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	365	4	369

Error

Counts

369 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
	0.1b	(/.f32 (/.f32 (/.f32 1 s) (*.f32 (cbrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))) (cbrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))))) (cbrt.f32 (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2))))
	0.1b	(*.f32 (/.f32 1 (sqrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))))))) (/.f32 (/.f32 1 s) (sqrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))))))))
▶	0.1b	(/.f32 1 (fma.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) s (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))

Compiler

Compiled 13367 to 4187 computations (68.7% saved)

localize39.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2)
✓	0.0b	(/.f32 1 (fma.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) s (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
	0.0b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.0b	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))

series155.0ms (2.4%)

Counts

3 → 40

Calls

3 calls:

109.0ms	(/.f32 1 (fma.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) s (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
27.0ms	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))
19.0ms	(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary32`
20×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
18×	`times-frac_binary32`
8×	`add-exp-log_binary32`

Counts

3 → 79

Calls

3 calls:

12.0ms	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))
7.0ms	(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2)
4.0ms	(/.f32 1 (fma.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) s (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))

simplify115.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

449×	`cancel-sign-sub-inv_binary32`
367×	`fma-neg_binary32`
247×	`unswap-sqr_binary32`
246×	`associate-/l*_binary32`
242×	`times-frac_binary32`

Counts

119 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3160
1	368	2863
2	877	2846
3	2979	2846
4	4925	2846
5	4937	2846

prune271.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	233	3	236

Error

Counts

236 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
	0.1b	(/.f32 (/.f32 (/.f32 1 s) (*.f32 (cbrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))) (cbrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))))) (cbrt.f32 (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2))))
▶	0.0b	(/.f32 1 (+.f32 (.f32 2 s) (+.f32 (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))) (.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s))))

Compiler

Compiled 6341 to 2230 computations (64.8% saved)

localize47.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 1 (+.f32 (.f32 2 s) (+.f32 (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))) (.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s))))
	0.0b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.0b	(*.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s)
	0.0b	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))

series123.0ms (1.9%)

Counts

2 → 32

Calls

2 calls:

110.0ms	(/.f32 1 (+.f32 (.f32 2 s) (+.f32 (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))) (.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s))))
12.0ms	(*.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

12.0ms	(/.f32 1 (+.f32 (.f32 2 s) (+.f32 (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))) (.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s))))
8.0ms	(*.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s)

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

460×	`fma-neg_binary32`
424×	`cancel-sign-sub-inv_binary32`
318×	`associate-l_binary32`
282×	`associate-r_binary32`
267×	`fma-def_binary32`

Counts

87 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2670
1	312	2396
2	907	2384
3	3179	2384
4	4939	2384
5	5012	2384

prune276.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	237	3	240

Error

Counts

240 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
	0.1b	(/.f32 (/.f32 (/.f32 1 s) (*.f32 (cbrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))) (cbrt.f32 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))))) (cbrt.f32 (+.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fabs.f32 x) s))) (sqrt.f32 (/.f32 (fabs.f32 x) s))) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2))))
✓	0.0b	(/.f32 1 (+.f32 (.f32 2 s) (+.f32 (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))) (.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) s))))

Compiler

Compiled 7223 to 2467 computations (65.8% saved)

regimes1.4s (21.9%)

Accuracy

Total 0.0b remaining (21.6%)

Threshold costs 0.0b (21.6%)

Counts

251 → 1

Compiler

Compiled 32145 to 19741 computations (38.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
2×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	22	37
2	21	37

end1.0ms (0%)

Compiler: Compiled 25 to 15 computations (40% saved)

sample1.3s (20.9%)

Algorithm

1×

intervals

Results

633.0ms	8000×	body	128	valid
149.0ms	8000×	pre	128	true

Compiler

Compiled 172 to 94 computations (45.3% saved)

Details

analyze171.0ms (2.7%)

sample42.0ms (0.6%)

simplify76.0ms (1.2%)

prune4.0ms (0.1%)

localize49.0ms (0.8%)

series108.0ms (1.7%)

rewrite68.0ms (1.1%)

simplify251.0ms (3.9%)

prune417.0ms (6.5%)

localize54.0ms (0.8%)

series580.0ms (9%)

rewrite56.0ms (0.9%)

simplify176.0ms (2.7%)

prune441.0ms (6.8%)

localize39.0ms (0.6%)

series155.0ms (2.4%)

rewrite27.0ms (0.4%)

simplify115.0ms (1.8%)

prune271.0ms (4.2%)

localize47.0ms (0.7%)

series123.0ms (1.9%)

rewrite23.0ms (0.4%)

simplify109.0ms (1.7%)

prune276.0ms (4.3%)

regimes1.4s (21.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (20.9%)

Profiling