Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.8s (25.1%)

Results

732.0ms	6145×	body	128	valid
442.0ms	1096×	body	1024	valid
228.0ms	615×	body	512	valid
67.0ms	308×	body	256	valid
40.0ms	92×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify207.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune4.0ms (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

12.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series58.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

40.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
18.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite67.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

472×	`fma-def_binary64`
257×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`

Counts

2 → 74

Calls

2 calls:

65.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
65.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	261	30
2	3563	30
3	4908	30
0	0	0
1	0	0

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

935×	`times-frac_binary64`
498×	`cancel-sign-sub-inv_binary64`
367×	`sub-neg_binary64`
205×	`+-commutative_binary64`
189×	`associate-+r+_binary64`

Counts

122 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2358
1	749	2323
2	2913	2279
3	5252	2279

prune119.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	4	129

Error

0.0b

Counts

129 → 4

Alt Table

Status	Error	Program
	50.0b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
▶	12.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
	12.6b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
	51.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 4035 to 2574 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))
✓	0.1b	(pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3)
✓	0.1b	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
✓	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)

series745.0ms (10.4%)

Counts

4 → 96

Calls

4 calls:

609.0ms	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
87.0ms	(pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3)
31.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)
17.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))

rewrite146.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

863×	`prod-diff_binary64`
308×	`egg-rr`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`
154×	`add-sqr-sqrt_binary64`

Counts

4 → 308

Calls

4 calls:

133.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))
133.0ms	(pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3)
133.0ms	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
133.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	330	67
2	4040	67
3	5653	67
0	0	0
1	0	0

simplify240.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

433×	`+-commutative_binary64`
401×	`*-commutative_binary64`
371×	`fma-def_binary64`
369×	`associate-+r+_binary64`
280×	`associate-*r/_binary64`

Counts

404 → 393

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1301	17287
1	5006	17287

prune748.0ms (10.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	393	4	397

Error

0.0b

Counts

397 → 4

Alt Table

Status	Error	Program
	50.0b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	12.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
▶	12.6b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
	51.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 38994 to 27509 computations (29.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))
✓	0.2b	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))
✓	1.4b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)

series94.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

43.0ms

(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))

32.0ms

(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)

18.0ms

(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))))

rewrite139.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
294×	`egg-rr`
137×	`add-sqr-sqrt_binary64`
136×	`expm1-log1p-u_binary64`
135×	`log1p-expm1-u_binary64`

Counts

3 → 294

Calls

3 calls:

126.0ms

(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))))

126.0ms

(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))

126.0ms

(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	277	45
2	3658	45
3	5419	45
0	0	0
1	0	0

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

323×	`associate-+r+_binary64`
309×	`times-frac_binary64`
308×	`fma-def_binary64`
274×	`associate-+l+_binary64`
250×	`associate-/r*_binary64`

Counts

366 → 380

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	4150
1	1325	4067
2	5382	4067

prune1.0s (14.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	639	0	639
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	639	4	643

Error

0.0b

Counts

643 → 4

Alt Table

Status	Error	Program
▶	50.0b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	12.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
✓	12.6b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
	51.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 37481 to 22585 computations (39.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	2.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	3.6b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	7.7b	(/.f64 beta (*.f64 alpha alpha))

series135.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

40.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
34.0ms	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
32.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
28.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite240.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

320×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
173×	`add-log-exp_binary64`

Counts

4 → 141

Calls

4 calls:

235.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
235.0ms	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
235.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
235.0ms	(/.f64 beta (*.f64 alpha alpha))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	88
1	378	83
2	4706	83
3	5124	83
0	0	0
1	0	0

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-/l/_binary64`
318×	`sub-neg_binary64`
297×	`fma-def_binary64`
276×	`distribute-neg-frac_binary64`
203×	`distribute-rgt-neg-in_binary64`

Counts

237 → 171

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	1850
1	94	1820
2	244	1623
3	703	1484
4	2529	1387
5	4971	1387

prune328.0ms (4.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	170	5	175

Error

Counts

175 → 5

Alt Table

Status	Error	Program
	51.4b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	50.1b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 beta alpha) (/.f64 1 alpha))) (sqrt.f64 (+.f64 (/.f64 beta alpha) (/.f64 1 alpha))) (neg.f64 (fma.f64 2 (pow.f64 alpha -2) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2)))))
✓	50.0b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	12.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2) 3) 1/3)
✓	12.6b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)

Compiler

Compiled 6960 to 3382 computations (51.4% saved)

regimes620.0ms (8.7%)

Accuracy

Total 0.0b remaining (51.7%)

Threshold costs 0.0b (51.7%)

Counts

91 → 2

Compiler

Compiled 10145 to 7076 computations (30.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
6×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	78
1	42	78
2	52	78
3	58	78
4	61	78
5	60	78

end150.0ms (2.1%)

Compiler: Compiled 270 to 167 computations (38.1% saved)

Details

analyze2.0ms (0%)

sample1.8s (25.1%)

simplify207.0ms (2.9%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series58.0ms (0.8%)

rewrite67.0ms (0.9%)

simplify63.0ms (0.9%)

prune119.0ms (1.7%)

localize10.0ms (0.1%)

series745.0ms (10.4%)

rewrite146.0ms (2%)

simplify240.0ms (3.4%)

prune748.0ms (10.5%)

localize11.0ms (0.2%)

series94.0ms (1.3%)

rewrite139.0ms (2%)

simplify86.0ms (1.2%)

prune1.0s (14.4%)

localize14.0ms (0.2%)

series135.0ms (1.9%)

rewrite240.0ms (3.4%)

simplify70.0ms (1%)

prune328.0ms (4.6%)

regimes620.0ms (8.7%)

bsearch3.0ms (0%)

simplify9.0ms (0.1%)

end150.0ms (2.1%)

Profiling