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 (43.3%)

Results

848.0ms	6147×	body	128	valid
363.0ms	1059×	body	1024	valid
256.0ms	625×	body	512	valid
58.0ms	327×	body	256	valid
40.0ms	98×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify207.0ms (4.9%)

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

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

15.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.2b	(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))
✓	2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series52.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

35.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
17.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite20.0ms (0.5%)

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:

8.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
8.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify89.0ms (2.1%)

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

prune116.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	5	143

Error

0.0b

Counts

143 → 5

Alt Table

Status	Error	Program
	49.4b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	43.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
▶	15.2b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	47.6b	(-.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 4521 to 2785 computations (38.4% saved)

localize10.0ms (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 beta alpha) 2))))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.3b	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
✓	2.2b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

series96.0ms (2.3%)

Counts

3 → 72

Calls

3 calls:

45.0ms

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

33.0ms

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

18.0ms

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

rewrite2.0ms (0%)

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))))

simplify122.0ms (2.9%)

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

prune211.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	237	6	243

Error

0.0b

Counts

243 → 6

Alt Table

Status	Error	Program
	49.4b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
▶	15.2b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))) -1/2 1/2)
	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	47.6b	(-.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)))))
	15.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2))) (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)))
	43.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 8615 to 5707 computations (33.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))))
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))
✓	0.3b	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))
✓	2.2b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))) -1/2 1/2)

series110.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

41.0ms	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))
33.0ms	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))) -1/2 1/2)
18.0ms	(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))))
18.0ms	(/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

8.0ms	(/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))
0.0ms	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))) -1/2 1/2)
0.0ms	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))))

simplify108.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

336×	`fma-def_binary64`
317×	`times-frac_binary64`
264×	`associate-/r*_binary64`
249×	`associate-/l*_binary64`
226×	`associate--l+_binary64`

Counts

182 → 171

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	502	7036
1	1542	6792
2	5064	6792

prune165.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	171	6	177

Error

0.0b

Counts

177 → 6

Alt Table

Status	Error	Program
	49.4b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
✓	15.2b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))) -1/2 1/2)
▶	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	47.6b	(-.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)))))
	15.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2))) (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)))
	43.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 6651 to 4552 computations (31.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
✓	4.9b	(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

series110.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

58.0ms

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

33.0ms

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

19.0ms

(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64`
62×	`exp-prod_binary64`
50×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
32×	`log-pow_binary64`

Counts

3 → 98

Calls

3 calls:

10.0ms

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

10.0ms

(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

0.0ms

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

simplify99.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

312×	`fma-def_binary64`
310×	`times-frac_binary64`
256×	`associate-+l+_binary64`
254×	`associate-/r*_binary64`
239×	`associate-/l*_binary64`

Counts

170 → 217

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	502	5734
1	1453	5579
2	5145	5579

prune316.0ms (7.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	312	7	319

Error

0.0b

Counts

319 → 7

Alt Table

Status	Error	Program
	49.4b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
✓	15.2b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))))) -1/2 1/2)
✓	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	47.6b	(-.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)))))
	15.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2))) (cbrt.f64 (fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)))
	15.2b	(fma.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha)))) 3))) -1/2 1/2)
	43.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 10490 to 6678 computations (36.3% saved)

regimes314.0ms (7.4%)

Accuracy

Total 0.3b remaining (87.8%)

Threshold costs 0.3b (87.8%)

Counts

48 → 2

Compiler

Compiled 5658 to 4174 computations (26.2% saved)

bsearch3.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-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	47	80
2	61	80
3	76	80
4	83	80
5	85	80
6	83	80

end181.0ms (4.3%)

Compiler: Compiled 351 to 224 computations (36.2% saved)

Details

analyze2.0ms (0%)

sample1.8s (43.3%)

simplify207.0ms (4.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series52.0ms (1.2%)

rewrite20.0ms (0.5%)

simplify89.0ms (2.1%)

prune116.0ms (2.7%)

localize10.0ms (0.2%)

series96.0ms (2.3%)

rewrite2.0ms (0%)

simplify122.0ms (2.9%)

prune211.0ms (5%)

localize10.0ms (0.2%)

series110.0ms (2.6%)

rewrite14.0ms (0.3%)

simplify108.0ms (2.5%)

prune165.0ms (3.9%)

localize11.0ms (0.3%)

series110.0ms (2.6%)

rewrite29.0ms (0.7%)

simplify99.0ms (2.3%)

prune316.0ms (7.4%)

regimes314.0ms (7.4%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end181.0ms (4.3%)

Profiling