Details

analyze1.1s (22.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
0%	56.2%	43.8%	3
0%	56.2%	43.8%	4
3.5%	52.7%	43.8%	5
7%	49.2%	43.8%	6
14%	42.1%	43.8%	7
15.8%	40.4%	43.8%	8
17.8%	38.4%	43.8%	9
18.8%	37.4%	43.8%	10
19.8%	36.4%	43.8%	11
20.3%	35.9%	43.8%	12
20.9%	35.3%	43.8%	13
21.4%	34.8%	43.8%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.8s (36.7%)

Results

750.0ms	6134×	body	128	valid
464.0ms	1079×	body	1024	valid
198.0ms	609×	body	512	valid
70.0ms	336×	body	256	valid
48.0ms	98×	body	2048	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify208.0ms (4.2%)

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

16.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series57.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
20.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite14.0ms (0.3%)

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:

9.0ms	(/.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)

simplify94.0ms (1.9%)

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

prune123.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	5	143

Error

0.0b

Counts

143 → 5

Alt Table

Status	Error	Program
▶	16.1b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	45.7b	(/.f64 (+.f64 beta 1) alpha)
✓	16.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	48.1b	(-.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)))))
	16.1b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 4389 to 2703 computations (38.4% saved)

localize11.0ms (0.2%)

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))))
✓	0.3b	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
✓	1.4b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

series100.0ms (2%)

Counts

3 → 72

Calls

3 calls:

45.0ms

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

35.0ms

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

20.0ms

(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

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

0.0ms

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

0.0ms

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

simplify84.0ms (1.7%)

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

prune252.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	238	5	243

Error

0.0b

Counts

243 → 5

Alt Table

Status	Error	Program
✓	16.1b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	45.7b	(/.f64 (+.f64 beta 1) alpha)
✓	16.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	48.1b	(-.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)))))
▶	16.1b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 8369 to 5547 computations (33.7% saved)

localize14.0ms (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	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.4b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

series94.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

50.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
43.0ms	(log.f64 (exp.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×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-prod_binary64`

Counts

2 → 32

Calls

2 calls:

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

simplify111.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

363×	`sub-neg_binary64`
288×	`times-frac_binary64`
253×	`fma-def_binary64`
251×	`+-commutative_binary64`
247×	`associate-+r+_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4045
1	1105	3894
2	4579	3852
3	5169	3852

prune271.0ms (5.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	255	5	260

Error

0.0b

Counts

260 → 5

Alt Table

Status	Error	Program
✓	16.1b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
▶	45.7b	(/.f64 (+.f64 beta 1) alpha)
✓	16.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	48.1b	(-.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)))))
✓	16.1b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 9345 to 6225 computations (33.4% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 beta 1) alpha)

series7.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(/.f64 (+.f64 beta 1) alpha)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

1 → 35

Calls

1 calls:

4.0ms

(/.f64 (+.f64 beta 1) alpha)

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

657×	`distribute-rgt-in_binary64`
554×	`distribute-lft-in_binary64`
413×	`associate-+l+_binary64`
338×	`unsub-neg_binary64`
305×	`associate-+r+_binary64`

Counts

47 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	585
1	134	551
2	294	551
3	688	518
4	1731	518
5	3257	518
6	4763	518
7	5090	518

prune31.0ms (0.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	56	6	62

Error

Counts

62 → 6

Alt Table

Status	Error	Program
✓	16.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	46.0b	(/.f64 (/.f64 (+.f64 beta 1) (sqrt.f64 alpha)) (sqrt.f64 alpha))
✓	16.1b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
✓	45.7b	(/.f64 (+.f64 beta 1) alpha)
	48.1b	(-.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)))))
✓	16.1b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 793 to 512 computations (35.4% saved)

regimes301.0ms (6.1%)

Accuracy

Total -0.0b remaining (-0.2%)

Threshold costs -0.0b (-0.2%)

Counts

41 → 2

Compiler

Compiled 3885 to 2926 computations (24.7% 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	31	76
1	41	76
2	55	76
3	70	76
4	77	76
5	79	76
6	77	76

end117.0ms (2.4%)

Compiler: Compiled 231 to 141 computations (39% saved)

Details

analyze1.1s (22.8%)

sample1.8s (36.7%)

simplify208.0ms (4.2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series57.0ms (1.2%)

rewrite14.0ms (0.3%)

simplify94.0ms (1.9%)

prune123.0ms (2.5%)

localize11.0ms (0.2%)

series100.0ms (2%)

rewrite2.0ms (0%)

simplify84.0ms (1.7%)

prune252.0ms (5.1%)

localize14.0ms (0.3%)

series94.0ms (1.9%)

rewrite4.0ms (0.1%)

simplify111.0ms (2.3%)

prune271.0ms (5.5%)

localize3.0ms (0.1%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify80.0ms (1.6%)

prune31.0ms (0.6%)

regimes301.0ms (6.1%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end117.0ms (2.4%)

Profiling