Details

analyze10.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0.1%	0%	99.9%	1

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample3.0s (52%)

Results

2.8s	8254×	body	128	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-def_binary32`
155×	`fma-neg_binary32`
47×	`cancel-sign-sub-inv_binary32`
34×	`sub-neg_binary32`
26×	`unsub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	8
2	35	8
3	63	8
4	142	8
5	262	8
6	381	8
7	434	8
8	458	8
9	463	8
10	428	8

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize30.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(fma.f32 ux maxCos (-.f32 1 ux))

rewrite96.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

583×	`log1p-expm1-u_binary32`
583×	`expm1-log1p-u_binary32`
265×	`log-prod_binary32`
227×	`prod-diff_binary32`
110×	`expm1-udef_binary32`

Counts

1 → 31

Calls

1 calls:

94.0ms

(fma.f32 ux maxCos (-.f32 1 ux))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	123	8
2	1454	8
3	4960	8
4	4965	8
0	0	0
1	0	0

simplify46.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

161×	`fma-def_binary32`
149×	`fma-neg_binary32`
26×	`associate--r+_binary32`
26×	`sub-neg_binary32`
24×	`distribute-rgt-in_binary32`

Counts

55 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171

prune64.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

0.0b

Counts

40 → 5

Alt Table

Status	Error	Program
▶	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
	0.6b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))
	0.5b	(log.f32 (+.f32 1 (expm1.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
	0.4b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)

Compiler

Compiled 522 to 333 computations (36.2% saved)

localize46.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

series38.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
8.0ms	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

rewrite126.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

658×	`expm1-log1p-u_binary32`
657×	`log1p-expm1-u_binary32`
251×	`prod-diff_binary32`
155×	`fma-udef_binary32`
125×	`expm1-udef_binary32`

Counts

2 → 64

Calls

2 calls:

124.0ms	(log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
124.0ms	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	142	18
2	1646	18
3	4889	18
4	4981	18
5	4965	18
0	0	0
1	0	0

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary32`
382×	`times-frac_binary32`
342×	`fma-neg_binary32`
272×	`sub-neg_binary32`
196×	`distribute-rgt-in_binary32`

Counts

112 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	1217
1	569	1147
2	2146	1123
3	4991	1122
4	5169	1122

prune260.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	157	5	162

Error

Counts

162 → 5

Alt Table

Status	Error	Program
✓	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
	0.6b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
	0.4b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)
▶	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))

Compiler

Compiled 2871 to 1913 computations (33.4% saved)

localize85.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (fma.f32 ux ux ux))
✓	0.0b	(-.f32 1 (pow.f32 ux 3))
✓	0.1b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
✓	0.4b	(/.f32 1 (+.f32 1 (fma.f32 ux ux ux)))

series116.0ms (2%)

Counts

4 → 51

Calls

4 calls:

101.0ms	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
6.0ms	(/.f32 1 (+.f32 1 (fma.f32 ux ux ux)))
5.0ms	(-.f32 1 (pow.f32 ux 3))
4.0ms	(+.f32 1 (fma.f32 ux ux ux))

rewrite97.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

706×	`prod-diff_binary32`
221×	`expm1-udef_binary32`
220×	`log1p-udef_binary32`
127×	`add-sqr-sqrt_binary32`
121×	`log1p-expm1-u_binary32`

Counts

4 → 115

Calls

4 calls:

92.0ms	(+.f32 1 (fma.f32 ux ux ux))
92.0ms	(-.f32 1 (pow.f32 ux 3))
92.0ms	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
92.0ms	(/.f32 1 (+.f32 1 (fma.f32 ux ux ux)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	261	49
2	3085	49
3	5044	49
0	0	0
1	0	0

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary32`
493×	`unswap-sqr_binary32`
336×	`div-sub_binary32`
279×	`fma-def_binary32`
271×	`associate-l_binary32`

Counts

166 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	772
1	119	680
2	302	680
3	730	678
4	2202	678
5	4568	678
6	4975	678

prune241.0ms (4.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	149	5	154

Error

Counts

154 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux)))) (*.f32 ux maxCos))
✓	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
✓	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
	0.4b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)

Compiler

Compiled 3326 to 1963 computations (41% saved)

localize88.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f32 1 (pow.f32 ux 3))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux))))
✓	0.1b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux)))) (*.f32 ux maxCos))
✓	0.3b	(log1p.f32 (fma.f32 ux ux ux))

series265.0ms (4.6%)

Counts

3 → 48

Calls

3 calls:

251.0ms	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux)))) (*.f32 ux maxCos))
8.0ms	(exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux))))
5.0ms	(log1p.f32 (fma.f32 ux ux ux))

rewrite155.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`prod-diff_binary32`
402×	`fma-udef_binary32`
284×	`fma-def_binary32`
206×	`expm1-udef_binary32`
205×	`log1p-udef_binary32`

Counts

3 → 100

Calls

3 calls:

151.0ms	(exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux))))
151.0ms	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux)))) (*.f32 ux maxCos))
151.0ms	(log1p.f32 (fma.f32 ux ux ux))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	264	36
2	2754	36
3	4748	36
4	4805	36
5	5007	36
0	0	0
1	0	0

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary32`
505×	`associate-l_binary32`
476×	`sub-neg_binary32`
324×	`fma-neg_binary32`
317×	`cancel-sign-sub-inv_binary32`

Counts

148 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	950
1	213	748
2	535	704
3	1442	664
4	3630	664
5	5128	664

prune270.0ms (4.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	178	5	183

Error

Counts

183 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (exp.f32 (neg.f32 (log1p.f32 (fma.f32 ux ux ux)))) (*.f32 ux maxCos))
✓	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
✓	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
	0.4b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)

Compiler

Compiled 3786 to 2053 computations (45.8% saved)

regimes287.0ms (5%)

Accuracy

Total 0.0b remaining (75.7%)

Threshold costs 0.0b (75.7%)

Counts

33 → 1

Compiler

Compiled 2030 to 1489 computations (26.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	14	8
3	16	8
4	17	8
5	16	8

end63.0ms (1.1%)

Compiler: Compiled 90 to 63 computations (30% saved)

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171

Details

analyze10.0ms (0.2%)

sample3.0s (52%)

simplify28.0ms (0.5%)

prune5.0ms (0.1%)

localize30.0ms (0.5%)

series8.0ms (0.1%)

rewrite96.0ms (1.7%)

simplify46.0ms (0.8%)

prune64.0ms (1.1%)

localize46.0ms (0.8%)

series38.0ms (0.7%)

rewrite126.0ms (2.2%)

simplify107.0ms (1.9%)

prune260.0ms (4.5%)

localize85.0ms (1.5%)

series116.0ms (2%)

rewrite97.0ms (1.7%)

simplify106.0ms (1.8%)

prune241.0ms (4.2%)

localize88.0ms (1.5%)

series265.0ms (4.6%)

rewrite155.0ms (2.7%)

simplify117.0ms (2%)

prune270.0ms (4.7%)

regimes287.0ms (5%)

simplify2.0ms (0%)

end63.0ms (1.1%)

Profiling

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171