Details

analyze6.0ms (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)

sample1.6s (41.3%)

Results

1.5s	8254×	body	128	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify18.0ms (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

prune3.0ms (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)

localize14.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite71.0ms (1.9%)

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 → 32

Calls

1 calls:

70.0ms

(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

simplify25.0ms (0.6%)

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

56 → 40

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

prune39.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	5	41

Error

Counts

41 → 5

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))
	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)
	0.8b	(+.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))))))
	1.2b	(+.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))))))
	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 577 to 370 computations (35.9% saved)

localize23.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.2b	(sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))
✓	0.4b	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)

series13.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)
4.0ms	(sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))

rewrite96.0ms (2.5%)

Algorithm

2×	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 → 71

Calls

2 calls:

95.0ms	(sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))
94.0ms	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	168	19
2	1801	19
3	4999	19
4	4960	19
5	5005	19
0	0	0
1	0	0

simplify61.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

636×	`unswap-sqr_binary32`
467×	`cancel-sign-sub-inv_binary32`
464×	`sub-neg_binary32`
362×	`fma-neg_binary32`
344×	`associate-+l+_binary32`

Counts

119 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	934
1	132	807
2	397	725
3	1439	679
4	3491	679
5	4979	679

prune214.0ms (5.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)
	0.3b	(sqrt.f32 (+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))))
	0.8b	(+.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))))))
▶	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 1865 to 1204 computations (35.4% saved)

localize13.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite102.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

624×	`log1p-expm1-u_binary32`
624×	`expm1-log1p-u_binary32`
359×	`prod-diff_binary32`
278×	`fma-udef_binary32`
238×	`fma-def_binary32`

Counts

1 → 99

Calls

1 calls:

100.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1534	8
3	4984	8
4	4965	8
5	4971	8
0	0	0
1	0	0

simplify26.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

123 → 108

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

prune93.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)
▶	0.3b	(sqrt.f32 (+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))))
	0.8b	(+.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))))))
✓	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 1636 to 865 computations (47.1% saved)

localize53.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))
✓	0.1b	(+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2))
✓	0.2b	(sqrt.f32 (+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))))
✓	0.2b	(+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2))))

series69.0ms (1.8%)

Counts

4 → 84

Calls

4 calls:

39.0ms	(sqrt.f32 (+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))))
15.0ms	(+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2))))
12.0ms	(.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))
2.0ms	(+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2))

rewrite84.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`fma-neg_binary32`
271×	`expm1-udef_binary32`
271×	`log1p-udef_binary32`
156×	`add-sqr-sqrt_binary32`
151×	`log1p-expm1-u_binary32`

Counts

4 → 133

Calls

4 calls:

80.0ms	(.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))
80.0ms	(+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2))
80.0ms	(sqrt.f32 (+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))))
80.0ms	(+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	86
1	321	74
2	3936	74
3	4938	74
0	0	0
1	0	0

simplify103.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

522×	`cancel-sign-sub-inv_binary32`
436×	`fma-neg_binary32`
432×	`times-frac_binary32`
244×	`fma-def_binary32`
226×	`sub-neg_binary32`

Counts

217 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	3368
1	586	2759
2	2250	2479
3	4589	2451
4	5338	2451

prune225.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Status	Error	Program
	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)
✓	0.3b	(sqrt.f32 (+.f32 (fma.f32 ux (fma.f32 2 maxCos -2) 1) (.f32 (.f32 ux ux) (+.f32 (fma.f32 maxCos maxCos 1) (*.f32 maxCos -2)))))
	0.8b	(+.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))))))
✓	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 7062 to 4823 computations (31.7% saved)

regimes814.0ms (21.3%)

Accuracy

Total 0.0b remaining (64.9%)

Threshold costs 0.0b (64.9%)

Counts

155 → 1

Compiler

Compiled 9851 to 7031 computations (28.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	17	15
2	19	15
3	20	15
4	19	15

end69.0ms (1.8%)

Compiler: Compiled 93 to 64 computations (31.2% 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

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

analyze6.0ms (0.2%)

sample1.6s (41.3%)

simplify18.0ms (0.5%)

prune3.0ms (0.1%)

localize14.0ms (0.4%)

series4.0ms (0.1%)

rewrite71.0ms (1.9%)

simplify25.0ms (0.6%)

prune39.0ms (1%)

localize23.0ms (0.6%)

series13.0ms (0.3%)

rewrite96.0ms (2.5%)

simplify61.0ms (1.6%)

prune214.0ms (5.6%)

localize13.0ms (0.3%)

series4.0ms (0.1%)

rewrite102.0ms (2.7%)

simplify26.0ms (0.7%)

prune93.0ms (2.4%)

localize53.0ms (1.4%)

series69.0ms (1.8%)

rewrite84.0ms (2.2%)

simplify103.0ms (2.7%)

prune225.0ms (5.9%)

regimes814.0ms (21.3%)

simplify2.0ms (0.1%)

end69.0ms (1.8%)

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

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