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)

sample1.9s (33.3%)

Results

659.0ms	6110×	body	128	valid
476.0ms	1068×	body	1024	valid
239.0ms	114×	body	2048	valid
171.0ms	628×	body	512	valid
77.0ms	336×	body	256	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify205.0ms (3.6%)

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

16.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.0b	(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))
✓	2.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series88.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

67.0ms	(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))

rewrite13.0ms (0.2%)

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

simplify89.0ms (1.6%)

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

prune113.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

0.0b

Counts

143 → 6

Alt Table

Status	Error	Program
	46.6b	(-.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)))))
	16.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
▶	16.1b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	16.0b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	44.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 4407 to 2709 computations (38.5% saved)

localize13.0ms (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 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
✓	0.0b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	2.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series119.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

85.0ms	(log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
34.0ms	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

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

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

464×	`times-frac_binary64`
383×	`associate-/r*_binary64`
362×	`fma-def_binary64`
307×	`associate-/l*_binary64`
201×	`associate-r_binary64`

Counts

70 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	407	4584
1	1378	4415
2	5011	4415

prune252.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	236	6	242

Error

0.0b

Counts

242 → 6

Alt Table

Status	Error	Program
	46.6b	(-.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)))))
	16.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
▶	16.1b	(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
✓	16.0b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	44.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 9898 to 6721 computations (32.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	0.0b	(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
✓	0.2b	(exp.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))
	2.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series518.0ms (9.1%)

Counts

3 → 72

Calls

3 calls:

376.0ms

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

107.0ms

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

35.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`

Counts

3 → 42

Calls

3 calls:

2.0ms

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

1.0ms

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

0.0ms

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

simplify184.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

868×	`associate-/l*_binary64`
302×	`*-commutative_binary64`
296×	`+-commutative_binary64`
256×	`fma-def_binary64`
242×	`associate-+r+_binary64`

Counts

114 → 163

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	979	13007
1	3443	12705
2	5980	12705

prune437.0ms (7.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	209	6	215

Error

0.0b

Counts

215 → 6

Alt Table

Status	Error	Program
▶	16.1b	(expm1.f64 (exp.f64 (log1p.f64 (expm1.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))))
	46.6b	(-.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)))))
	16.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
✓	16.0b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	44.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 18578 to 13964 computations (24.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (exp.f64 (log1p.f64 (expm1.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))))
✓	0.2b	(exp.f64 (log1p.f64 (expm1.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))))
✓	2.3b	(log1p.f64 (expm1.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	2.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series450.0ms (7.9%)

Counts

3 → 72

Calls

3 calls:

316.0ms

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

99.0ms

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

34.0ms

(expm1.f64 (exp.f64 (log1p.f64 (expm1.f64 (log.f64 (log1p.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×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
4×	`log1p-expm1-u_binary64`

Counts

3 → 36

Calls

3 calls:

1.0ms

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

0.0ms

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

0.0ms

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

simplify175.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

868×	`associate-/l*_binary64`
302×	`*-commutative_binary64`
297×	`+-commutative_binary64`
256×	`fma-def_binary64`
242×	`associate-+r+_binary64`

Counts

108 → 155

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	970	12844
1	3440	12536
2	5976	12536

prune419.0ms (7.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	201	6	207

Error

0.0b

Counts

207 → 6

Alt Table

Status	Error	Program
	46.6b	(-.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)))))
	16.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
	16.1b	(exp.f64 (log.f64 (expm1.f64 (exp.f64 (log1p.f64 (expm1.f64 (log.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))))))
✓	16.0b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	44.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))

Compiler

Compiled 18437 to 13948 computations (24.3% saved)

regimes471.0ms (8.3%)

Accuracy

Total 0.3b remaining (83.7%)

Threshold costs 0.3b (83.7%)

Counts

78 → 2

Compiler

Compiled 7418 to 5829 computations (21.4% saved)

bsearch4.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	78
1	37	78
2	48	78
3	61	78
4	67	78
5	69	78
6	67	78

end109.0ms (1.9%)

Compiler: Compiled 237 to 143 computations (39.7% saved)

Details

analyze2.0ms (0%)

sample1.9s (33.3%)

simplify205.0ms (3.6%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series88.0ms (1.5%)

rewrite13.0ms (0.2%)

simplify89.0ms (1.6%)

prune113.0ms (2%)

localize13.0ms (0.2%)

series119.0ms (2.1%)

rewrite2.0ms (0%)

simplify75.0ms (1.3%)

prune252.0ms (4.4%)

localize15.0ms (0.3%)

series518.0ms (9.1%)

rewrite5.0ms (0.1%)

simplify184.0ms (3.2%)

prune437.0ms (7.7%)

localize16.0ms (0.3%)

series450.0ms (7.9%)

rewrite3.0ms (0.1%)

simplify175.0ms (3.1%)

prune419.0ms (7.4%)

regimes471.0ms (8.3%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end109.0ms (1.9%)

Profiling