Details

analyze2.0ms (0.1%)

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)

sample299.0ms (7.6%)

Algorithm

1×

intervals

Results

8.0ms	173×	body	128	valid
6.0ms	39×	body	1024	valid
5.0ms	256×	pre	128	true
3.0ms	21×	body	512	valid
2.0ms	8×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify207.0ms (5.2%)

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

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

19.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.8b	(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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series55.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

36.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
19.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

12.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify93.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune128.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
▶	19.8b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	19.8b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.6b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	42.4b	(-.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)))))

Compiler

Compiled 4325 to 2659 computations (38.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))
✓	0.4b	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
✓	2.1b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

series109.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

50.0ms

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

36.0ms

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

19.0ms

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

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms

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

0.0ms

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

0.0ms

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

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

309×	`times-frac_binary64`
309×	`fma-def_binary64`
276×	`associate-+l+_binary64`
250×	`associate-/r*_binary64`
233×	`associate-/l*_binary64`

Counts

104 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	4807
1	1373	4631
2	5006	4631

prune200.0ms (5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	238	4	242

Error

0.0b

Counts

242 → 4

Alt Table

Status	Error	Program
✓	19.8b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
▶	19.8b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.6b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	42.4b	(-.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)))))

Compiler

Compiled 8305 to 5503 computations (33.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.2b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	1.3b	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series182.0ms (4.6%)

Counts

2 → 48

Calls

2 calls:

147.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
35.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify101.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

594×	`times-frac_binary64`
585×	`associate-/r*_binary64`
539×	`fma-def_binary64`
383×	`associate-/l*_binary64`
182×	`+-commutative_binary64`

Counts

79 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	556	6288
1	1886	6047
2	5229	6047

prune293.0ms (7.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	256	3	259
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	258	5	263

Error

0.0b

Counts

263 → 5

Alt Table

Status	Error	Program
	42.4b	(-.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)))))
	47.8b	(exp.f64 (neg.f64 (/.f64 (+.f64 alpha 1) beta)))
✓	19.8b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	20.3b	(.f64 (.f64 (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))) (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
▶	19.8b	(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 12507 to 8617 computations (31.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.2b	(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	1.3b	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series165.0ms (4.2%)

Counts

1 → 24

Calls

1 calls:

165.0ms

(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow-unpow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

1 → 24

Calls

1 calls:

2.0ms

(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

simplify90.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

298×	`times-frac_binary64`
294×	`sub-neg_binary64`
271×	`associate-/r*_binary64`
239×	`associate-/l*_binary64`
232×	`fma-def_binary64`

Counts

48 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	3718
1	1016	3263
2	4394	3176
3	5048	3176

prune370.0ms (9.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	279	5	284

Error

0.0b

Counts

284 → 5

Alt Table

Status	Error	Program
	42.4b	(-.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)))))
	47.8b	(exp.f64 (neg.f64 (/.f64 (+.f64 alpha 1) beta)))
✓	19.8b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	20.2b	(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	20.9b	(.f64 (pow.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (pow.f64 (cbrt.f64 (E.f64)) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))

Compiler

Compiled 15264 to 10494 computations (31.3% saved)

regimes286.0ms (7.2%)

Accuracy

Total 0.1b remaining (63.4%)

Threshold costs 0.1b (63.4%)

Counts

47 → 2

Compiler

Compiled 3756 to 2937 computations (21.8% saved)

bsearch1.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	43	80
2	57	80
3	72	80
4	79	80
5	81	80
6	79	80

end2.0ms (0.1%)

Compiler: Compiled 56 to 32 computations (42.9% saved)

sample1.2s (30.6%)

Algorithm

1×

intervals

Results

281.0ms	5937×	body	128	valid
204.0ms	1051×	body	1024	valid
183.0ms	8000×	pre	128	true
80.0ms	601×	body	512	valid
26.0ms	314×	body	256	valid
19.0ms	97×	body	2048	valid

Compiler

Compiled 208 to 132 computations (36.5% saved)

Details

analyze2.0ms (0.1%)

sample299.0ms (7.6%)

simplify207.0ms (5.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series55.0ms (1.4%)

rewrite17.0ms (0.4%)

simplify93.0ms (2.4%)

prune128.0ms (3.2%)

localize11.0ms (0.3%)

series109.0ms (2.8%)

rewrite2.0ms (0.1%)

simplify84.0ms (2.1%)

prune200.0ms (5%)

localize10.0ms (0.3%)

series182.0ms (4.6%)

rewrite4.0ms (0.1%)

simplify101.0ms (2.6%)

prune293.0ms (7.4%)

localize12.0ms (0.3%)

series165.0ms (4.2%)

rewrite3.0ms (0.1%)

simplify90.0ms (2.3%)

prune370.0ms (9.4%)

regimes286.0ms (7.2%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end2.0ms (0.1%)

sample1.2s (30.6%)

Profiling