Details

analyze125.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.5%	98.5%	0
0%	1.5%	98.5%	1
0%	1.5%	98.5%	2
0.8%	0.8%	98.5%	3
0.8%	0.8%	98.5%	4
1.2%	0.4%	98.5%	5
1.2%	0.4%	98.5%	6
1.4%	0.2%	98.5%	7
1.4%	0.2%	98.5%	8
1.4%	0.1%	98.5%	9
1.4%	0.1%	98.5%	10
1.5%	0%	98.5%	11
1.5%	0%	98.5%	12
1.5%	0%	98.5%	13
1.5%	0%	98.5%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.1s (33.4%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

175×	`fma-neg_binary32`
156×	`fma-def_binary32`
46×	`cancel-sign-sub-inv_binary32`
46×	`sub-neg_binary32`
29×	`distribute-rgt-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	13.1b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize20.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))

series327.0ms (5.3%)

Counts

2 → 36

Calls

2 calls:

322.0ms	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
4.0ms	(log1p.f32 (*.f32 u -4))

rewrite158.0ms (2.6%)

Algorithm

2×	egg-rewrite

Rules

40×	`egg`
35×	`egg`

Counts

2 → 75

Calls

2 calls:

79.0ms	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
77.0ms	(log1p.f32 (*.f32 u -4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	162	9
2	1583	9
3	4853	9
4	5062	9
0	5	6
1	98	6
2	1032	6
3	4713	6
4	4952	6

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary32`
530×	`fma-def_binary32`
369×	`sub-neg_binary32`
321×	`unsub-neg_binary32`
219×	`associate-+l+_binary32`

Counts

111 → 123

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	726
1	335	675
2	998	632
3	2998	621
4	4495	618
5	4993	618
6	4943	618

prune77.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	118	7	125

Error

0.0b

Counts

125 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	1.6b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	1.2b	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	1.6b	(.f32 s (neg.f32 (fma.f32 u (+.f32 -4 (.f32 u -8)) (.f32 (pow.f32 u 3) (-.f32 -64/3 (.f32 64 u))))))
	12.2b	(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
▶	0.8b	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))
	13.1b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 1947 to 1471 computations (24.4% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))
✓	0.8b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

series381.0ms (6.2%)

Counts

3 → 48

Calls

3 calls:

316.0ms	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))
45.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)
19.0ms	(cbrt.f32 (log1p.f32 (*.f32 u -4)))

rewrite202.0ms (3.3%)

Algorithm

3×	egg-rewrite

Rules

37×	`egg`
31×	`egg`
29×	`egg`

Counts

3 → 97

Calls

3 calls:

82.0ms	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
71.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)
48.0ms	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	6
1	146	6
2	1476	6
3	4867	6
4	4927	6
0	11	11
1	210	9
2	2026	9
3	4947	9
0	6	8
1	115	8
2	1216	8
3	4852	8
4	5662	8

simplify147.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

372×	`fma-def_binary32`
275×	`associate-+r+_binary32`
227×	`+-commutative_binary32`
224×	`sub-neg_binary32`
222×	`associate-/r*_binary32`

Counts

145 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	305	2698
1	1029	2419
2	3820	2383
3	4914	2305
4	4985	2305
5	4937	2305

prune171.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	224	8	232

Error

0.0b

Counts

232 → 8

Alt Table

Status	Error	Program
▶	1.2b	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	1.6b	(.f32 s (neg.f32 (fma.f32 u (+.f32 -4 (.f32 u -8)) (.f32 (pow.f32 u 3) (-.f32 -64/3 (.f32 64 u))))))
	1.5b	(.f32 s (neg.f32 (+.f32 (.f32 (.f32 u -4) (+.f32 (.f32 u 2) (.f32 16 (pow.f32 u 3)))) (.f32 (+.f32 (.f32 16/3 (.f32 u u)) 1) (*.f32 u -4)))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	12.2b	(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓	0.8b	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))
	1.6b	(fma.f32 8 (.f32 u (.f32 u s)) (fma.f32 64/3 (.f32 (pow.f32 u 3) s) (fma.f32 4 (.f32 u s) (.f32 64 (.f32 s (pow.f32 u 4))))))
	13.1b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 5942 to 4730 computations (20.4% saved)

localize44.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
✓	0.3b	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
✓	0.5b	(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)
✓	0.7b	(pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3)

series397.0ms (6.5%)

Counts

4 → 60

Calls

4 calls:

308.0ms	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
52.0ms	(pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3)
33.0ms	(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)
3.0ms	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

rewrite210.0ms (3.4%)

Algorithm

4×	egg-rewrite

Rules

43×	`egg`
34×	`egg`
27×	`egg`
26×	`egg`

Counts

4 → 130

Calls

4 calls:

56.0ms	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
52.0ms	(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)
50.0ms	(pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3)
49.0ms	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	221	9
2	2034	9
3	4975	9
0	9	13
1	174	11
2	1683	11
3	4984	11
0	12	6
1	241	6
2	2056	6
3	5016	6
0	15	28
1	309	9
2	2613	9
3	4876	9

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

566×	`times-frac_binary32`
338×	`cancel-sign-sub-inv_binary32`
323×	`fma-def_binary32`
263×	`distribute-neg-in_binary32`
210×	`sub-neg_binary32`

Counts

190 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	2588
1	912	2356
2	3025	2290
3	5023	2290

prune167.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	221	8	229

Error

0.0b

Counts

229 → 8

Alt Table

Status	Error	Program
▶	0.4b	(.f32 s (neg.f32 (.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	1.6b	(fma.f32 8 (.f32 u (.f32 u s)) (fma.f32 64/3 (.f32 (pow.f32 u 3) s) (fma.f32 4 (.f32 u s) (.f32 64 (.f32 s (pow.f32 u 4))))))
	1.5b	(.f32 s (neg.f32 (+.f32 (.f32 (.f32 u -4) (+.f32 (.f32 u 2) (.f32 16 (pow.f32 u 3)))) (.f32 (+.f32 (.f32 16/3 (.f32 u u)) 1) (*.f32 u -4)))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
	12.2b	(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓	0.8b	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))
✓	1.2b	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	13.1b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 6059 to 4922 computations (18.8% saved)

localize37.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 s (neg.f32 (.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
✓	0.3b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
✓	0.5b	(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

series322.0ms (5.2%)

Counts

3 → 48

Calls

3 calls:

312.0ms

(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))

6.0ms

(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

3.0ms

(*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

rewrite184.0ms (3%)

Algorithm

3×	egg-rewrite

Rules

37×	`egg`
35×	`egg`
31×	`egg`

Counts

3 → 103

Calls

3 calls:

54.0ms

(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))

49.0ms

(*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

45.0ms

(pow.f32 (log1p.f32 (*.f32 u -4)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	141	9
2	1363	9
3	5004	9
0	10	6
1	178	6
2	1671	6
3	4974	6
0	13	11
1	246	9
2	2230	9
3	5197	9

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

477×	`fma-neg_binary32`
282×	`fma-def_binary32`
278×	`cancel-sign-sub-inv_binary32`
243×	`sub-neg_binary32`
200×	`associate-l_binary32`

Counts

151 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	1385
1	665	1304
2	2217	1214
3	4787	1210
4	5086	1210

prune268.0ms (4.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	228	7	235

Error

0.0b

Counts

235 → 7

Alt Table

Status	Error	Program
	1.3b	(.f32 s (neg.f32 (.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2)) (+.f32 (.f32 (+.f32 (.f32 (pow.f32 u 3) 280/81) 1) (cbrt.f32 (.f32 u -4))) (.f32 (cbrt.f32 (.f32 u -4)) (+.f32 (.f32 u 2/3) (.f32 (*.f32 u u) 4/3)))))))
	12.2b	(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓	0.2b	(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
✓	0.8b	(.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3)))
✓	1.2b	(.f32 s (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4))))))
	1.6b	(fma.f32 8 (.f32 u (.f32 u s)) (fma.f32 64/3 (.f32 (pow.f32 u 3) s) (fma.f32 4 (.f32 u s) (.f32 64 (.f32 s (pow.f32 u 4))))))
	13.1b	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 5661 to 4541 computations (19.8% saved)

regimes419.0ms (6.8%)

Accuracy

Total 0.1b remaining (64.1%)

Threshold costs 0.1b (64.1%)

Counts

58 → 1

Compiler

Compiled 7492 to 5789 computations (22.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	8	11
1	16	11
2	23	11
3	29	11
4	32	11
5	33	11
6	33	11

end106.0ms (1.7%)

Compiler: Compiled 150 to 117 computations (22% saved)

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11

Details

analyze125.0ms (2%)

sample2.1s (33.4%)

simplify25.0ms (0.4%)

prune4.0ms (0.1%)

localize20.0ms (0.3%)

series327.0ms (5.3%)

rewrite158.0ms (2.6%)

simplify93.0ms (1.5%)

prune77.0ms (1.2%)

localize29.0ms (0.5%)

series381.0ms (6.2%)

rewrite202.0ms (3.3%)

simplify147.0ms (2.4%)

prune171.0ms (2.8%)

localize44.0ms (0.7%)

series397.0ms (6.5%)

rewrite210.0ms (3.4%)

simplify90.0ms (1.5%)

prune167.0ms (2.7%)

localize37.0ms (0.6%)

series322.0ms (5.2%)

rewrite184.0ms (3%)

simplify92.0ms (1.5%)

prune268.0ms (4.4%)

regimes419.0ms (6.8%)

simplify3.0ms (0%)

end106.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	10	14
1	24	11
2	38	11
3	64	11
4	83	11
5	110	11
6	144	11
7	194	11
8	244	11
9	291	11
10	319	11
11	362	11
12	401	11
13	478	11
14	491	11
15	443	11