Details

analyze104.0ms (2.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.3s (34%)

Results

639.0ms	6469×	body	128	valid
244.0ms	659×	body	1024	valid
172.0ms	687×	body	512	valid
72.0ms	435×	body	256	valid
2.0ms	6×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify200.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

15.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	26.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	15.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series21.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

6.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify77.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune75.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	28.9b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
	27.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
▶	15.2b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

Compiler

Compiled 1898 to 1302 computations (31.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
✓	3.0b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

series22.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
11.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

rewrite56.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
18×	`associate-l_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 63

Calls

2 calls:

45.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
7.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

simplify89.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-def_binary64`
614×	`distribute-rgt-in_binary64`
462×	`fma-neg_binary64`
427×	`times-frac_binary64`
212×	`cancel-sign-sub-inv_binary64`

Counts

111 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	1963
1	635	1902
2	2032	1877
3	4769	1877
4	5048	1877

prune90.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	141	4	145

Error

0.0b

Counts

145 → 4

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	28.9b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
▶	27.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	15.2b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

Compiler

Compiled 2754 to 1902 computations (30.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 y y))
✓	0.9b	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
✓	4.4b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	9.0b	(/.f64 x (*.f64 y y))

series108.0ms (2.9%)

Counts

4 → 84

Calls

4 calls:

46.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
35.0ms	(/.f64 x (*.f64 y y))
24.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
2.0ms	(/.f64 1 (*.f64 y y))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
26×	`distribute-lft-out_binary64`
24×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

21.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
12.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
3.0ms	(/.f64 1 (*.f64 y y))
3.0ms	(/.f64 x (*.f64 y y))

simplify129.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
251×	`cancel-sign-sub-inv_binary64`
196×	`associate-/r/_binary64`
171×	`distribute-rgt-neg-in_binary64`
166×	`distribute-rgt-in_binary64`

Counts

230 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5463
1	643	4334
2	2435	3523
3	4370	3521
4	4967	3521

prune191.0ms (5.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	187	6	193

Error

Counts

193 → 6

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
▶	28.9b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
✓	27.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
	46.3b	(.f64 (sqrt.f64 (+.f64 x (.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1)))) (sqrt.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1)))))
✓	15.2b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	53.9b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (+.f64 (.f64 1 y) (.f64 (.f64 y y) (+.f64 x -1))) (.f64 (.f64 y y) y)))

Compiler

Compiled 6170 to 2881 computations (53.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	0.0b	(log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
✓	1.2b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
	15.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series75.0ms (2%)

Counts

2 → 48

Calls

2 calls:

63.0ms	(log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
12.0ms	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

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	(log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
0.0ms	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

simplify92.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-+r+_binary64`
391×	`+-commutative_binary64`
352×	`fma-def_binary64`
343×	`associate-+l+_binary64`
305×	`associate-/r*_binary64`

Counts

70 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	370	3684
1	1188	3584
2	4948	3584
3	5060	3584

prune167.0ms (4.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	191	6	197

Error

Counts

197 → 6

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	28.9b	(expm1.f64 (log1p.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
✓	27.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
	46.3b	(.f64 (sqrt.f64 (+.f64 x (.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1)))) (sqrt.f64 (+.f64 x (*.f64 (/.f64 (+.f64 x -1) y) (+.f64 (/.f64 1 y) -1)))))
✓	15.2b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	53.9b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (+.f64 (.f64 1 y) (.f64 (.f64 y y) (+.f64 x -1))) (.f64 (.f64 y y) y)))

Compiler

Compiled 6444 to 4511 computations (30% saved)

regimes688.0ms (18.6%)

Accuracy

Total 0.0b remaining (16.4%)

Threshold costs 0.0b (16.4%)

Counts

87 → 3

Compiler

Compiled 7232 to 4667 computations (35.5% saved)

bsearch40.0ms (1.1%)

Steps

Iters	Range		Point
9	69711.65277553875	5269054208681.35	245860.08583667743
10	-8518609560254452000.0	-39034.92590110535	-507940.76313948643

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`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	21	50
1	31	50
2	36	50
3	44	50
4	50	50
5	53	50
6	54	50
7	52	50

end114.0ms (3.1%)

Compiler: Compiled 190 to 129 computations (32.1% saved)

Details

analyze104.0ms (2.8%)

sample1.3s (34%)

simplify200.0ms (5.4%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite9.0ms (0.3%)

simplify77.0ms (2.1%)

prune75.0ms (2%)

localize10.0ms (0.3%)

series22.0ms (0.6%)

rewrite56.0ms (1.5%)

simplify89.0ms (2.4%)

prune90.0ms (2.4%)

localize11.0ms (0.3%)

series108.0ms (2.9%)

rewrite51.0ms (1.4%)

simplify129.0ms (3.5%)

prune191.0ms (5.1%)

localize9.0ms (0.2%)

series75.0ms (2%)

rewrite2.0ms (0%)

simplify92.0ms (2.5%)

prune167.0ms (4.5%)

regimes688.0ms (18.6%)

bsearch40.0ms (1.1%)

simplify4.0ms (0.1%)

end114.0ms (3.1%)

Profiling