Details

analyze6.0ms (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)

sample104.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 46 to 34 computations (26.1% 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)

localize19.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary32`
1×	`add-sqr-sqrt_binary32`
1×	`add-cube-cbrt_binary32`
1×	`add-cbrt-cube_binary32`
1×	`add-exp-log_binary32`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-neg_binary32`
470×	`times-frac_binary32`
313×	`distribute-rgt-in_binary32`
309×	`neg-sub0_binary32`
301×	`distribute-lft-in_binary32`

Counts

34 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	331
1	45	278
2	99	277
3	292	277
4	1097	277
5	2072	277
6	4492	277
7	5251	277

prune27.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	23	3	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
	0.3b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 299 to 182 computations (39.1% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 (*.f32 maxCos ux) ux)
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series10.2s (83.4%)

Counts

3 → 63

Calls

3 calls:

10.2s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
18.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
4.0ms	(-.f32 (*.f32 maxCos ux) ux)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary32`
6×	`add-sqr-sqrt_binary32`
6×	`add-cube-cbrt_binary32`
6×	`add-log-exp_binary32`
4×	`expm1-log1p-u_binary32`

Counts

3 → 46

Calls

3 calls:

3.0ms	(-.f32 (*.f32 maxCos ux) ux)
1.0ms	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
1.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary32`
308×	`sub-neg_binary32`
267×	`cancel-sign-sub-inv_binary32`
226×	`unswap-sqr_binary32`
223×	`fma-def_binary32`

Counts

109 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	2337
1	740	2054
2	3057	1971
3	4863	1971
4	5002	1971

prune83.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Error

Counts

147 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
	0.3b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
▶	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 2807 to 1464 computations (47.8% saved)

localize14.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary32`
11×	`add-sqr-sqrt_binary32`
9×	`prod-diff_binary32`
9×	`add-cube-cbrt_binary32`
3×	`cancel-sign-sub-inv_binary32`

Counts

1 → 31

Calls

1 calls:

3.0ms

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

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

528×	`associate-+l+_binary32`
373×	`associate-l_binary32`
331×	`fma-def_binary32`
297×	`associate-r_binary32`
275×	`exp-prod_binary32`

Counts

55 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	547
1	136	511
2	485	480
3	2155	478
4	4739	478
5	4961	478
6	4875	478

prune29.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	51	3	54

Error

Counts

54 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
▶	0.3b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 783 to 402 computations (48.7% saved)

localize22.0ms (0.2%)

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)))
✓	0.3b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

series21.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
5.0ms	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`add-cube-cbrt_binary32`
2×	`add-cbrt-cube_binary32`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
0.0ms	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary32`
382×	`times-frac_binary32`
272×	`sub-neg_binary32`
230×	`distribute-rgt-in_binary32`
187×	`cancel-sign-sub-inv_binary32`

Counts

70 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	1502
1	593	1392
2	2191	1367
3	5083	1367

prune70.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	118	3	121

Error

Counts

121 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.3b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 2277 to 1542 computations (32.3% saved)

regimes84.0ms (0.7%)

Accuracy

Total 0.0b remaining (77.3%)

Threshold costs 0.0b (77.3%)

Counts

21 → 1

Compiler

Compiled 798 to 617 computations (22.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample1.2s (9.6%)

Algorithm

1×

intervals

Results

336.0ms	7999×	body	128	valid
269.0ms	8000×	pre	128	true
0.0ms	1×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

Details

analyze6.0ms (0%)

sample104.0ms (0.8%)

simplify18.0ms (0.1%)

prune3.0ms (0%)

localize19.0ms (0.2%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify61.0ms (0.5%)

prune27.0ms (0.2%)

localize19.0ms (0.2%)

series10.2s (83.4%)

rewrite6.0ms (0.1%)

simplify109.0ms (0.9%)

prune83.0ms (0.7%)

localize14.0ms (0.1%)

series4.0ms (0%)

rewrite5.0ms (0%)

simplify83.0ms (0.7%)

prune29.0ms (0.2%)

localize22.0ms (0.2%)

series21.0ms (0.2%)

rewrite1.0ms (0%)

simplify55.0ms (0.4%)

prune70.0ms (0.6%)

regimes84.0ms (0.7%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (9.6%)

Profiling