Details

analyze5.0ms (0%)

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)

sample1.5s (6.4%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify18.0ms (0.1%)

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

prune3.0ms (0%)

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)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

rewrite72.0ms (0.3%)

Algorithm

1×	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:

71.0ms

(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

simplify22.0ms (0.1%)

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

prune31.0ms (0.1%)

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
	0.5b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)
	0.7b	(+.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))
	1.1b	(+.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (cbrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))) (log.f32 (cbrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.5b	(pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)

Compiler

Compiled 564 to 363 computations (35.6% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.2b	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.5b	(pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)

series327.0ms (1.4%)

Counts

2 → 16

Calls

2 calls:

292.0ms	(pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)
35.0ms	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))

rewrite95.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

710×	`log1p-expm1-u_binary32`
710×	`expm1-log1p-u_binary32`
216×	`prod-diff_binary32`
161×	`fma-udef_binary32`
135×	`log1p-udef_binary32`

Counts

2 → 66

Calls

2 calls:

94.0ms	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
94.0ms	(pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	169	18
2	1803	18
3	4999	18
4	4960	18
5	5005	18

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-def_binary32`
411×	`sub-neg_binary32`
400×	`associate-l_binary32`
357×	`associate-r_binary32`
269×	`unswap-sqr_binary32`

Counts

82 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	380
1	226	361
2	763	338
3	3538	332
4	5040	332

prune105.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	122	5	127

Error

Counts

127 → 5

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))
	0.7b	(+.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))
	0.5b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)
	0.5b	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3) 2)
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 1977 to 1333 computations (32.6% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4)
	0.2b	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.2b	(*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.3b	(.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))

series124.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

96.0ms

(*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

22.0ms

(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4)

5.0ms

(*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))

rewrite52.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary32`
864×	`expm1-log1p-u_binary32`
216×	`prod-diff_binary32`
103×	`add-log-exp_binary32`
102×	`add-cbrt-cube_binary32`

Counts

3 → 56

Calls

3 calls:

51.0ms

(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4)

51.0ms

(*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

51.0ms

(*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (*.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	70
1	230	30
2	2188	30
3	5521	30

simplify113.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary32`
568×	`associate-/r*_binary32`
477×	`times-frac_binary32`
288×	`associate-/l*_binary32`
211×	`*-commutative_binary32`

Counts

128 → 154

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	621	7909
1	2250	7246
2	5466	7246

prune471.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	253	5	258

Error

Counts

258 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))
	0.7b	(+.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))
	0.5b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)
▶	0.5b	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3) 2)
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 17303 to 12418 computations (28.2% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3)
✓	0.3b	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2)
✓	0.5b	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3) 2)

series18.8s (81.7%)

Counts

3 → 72

Calls

3 calls:

18.6s	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3) 2)
88.0ms	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2)
63.0ms	(pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3)

rewrite86.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

410×	`log-prod_binary32`
267×	`pow2_binary32`
226×	`prod-diff_binary32`
181×	`expm1-udef_binary32`
180×	`pow1/3_binary32`

Counts

3 → 103

Calls

3 calls:

84.0ms	(pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3)
84.0ms	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2)
84.0ms	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	261	29
2	2430	29
3	4944	29
4	4850	29

simplify109.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

378×	`fma-def_binary32`
352×	`sub-neg_binary32`
275×	`fma-neg_binary32`
263×	`+-commutative_binary32`
240×	`associate-/r*_binary32`

Counts

175 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	4672
1	1166	4458
2	4124	4284
3	4992	4284

prune323.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	253	5	258

Error

Counts

258 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/4) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))
	0.7b	(+.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))
	0.5b	(-.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)
✓	0.5b	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3/2) 1/3) 2)
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 7650 to 5236 computations (31.6% saved)

regimes555.0ms (2.4%)

Accuracy

Total 0.0b remaining (59.7%)

Threshold costs 0.0b (59.7%)

Counts

114 → 1

Compiler

Compiled 7770 to 5966 computations (23.2% 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

end66.0ms (0.3%)

Compiler: Compiled 105 to 75 computations (28.6% 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

analyze5.0ms (0%)

sample1.5s (6.4%)

simplify18.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series5.0ms (0%)

rewrite72.0ms (0.3%)

simplify22.0ms (0.1%)

prune31.0ms (0.1%)

localize20.0ms (0.1%)

series327.0ms (1.4%)

rewrite95.0ms (0.4%)

simplify43.0ms (0.2%)

prune105.0ms (0.5%)

localize32.0ms (0.1%)

series124.0ms (0.5%)

rewrite52.0ms (0.2%)

simplify113.0ms (0.5%)

prune471.0ms (2.1%)

localize35.0ms (0.2%)

series18.8s (81.7%)

rewrite86.0ms (0.4%)

simplify109.0ms (0.5%)

prune323.0ms (1.4%)

regimes555.0ms (2.4%)

simplify2.0ms (0%)

end66.0ms (0.3%)

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