Details

analyze189.0ms (4.9%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample44.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms

256×

body

128

valid

Compiler

Compiled 45 to 27 computations (40% saved)

simplify127.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune6.0ms (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

30.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.4b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize23.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 y 4)))
✓	2.7b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	29.8b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series60.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
15.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))
14.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
1.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))
1.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

simplify173.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
500×	`div-sub_binary64`
426×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
223×	`distribute-rgt-in_binary64`

Counts

121 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	2496
1	221	2296
2	581	2284
3	2083	2266
4	4490	2230
5	5508	2230

prune145.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

0.2b

Counts

112 → 5

Alt Table

Status	Error	Program
▶	30.4b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	30.4b	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.0b	-1
	30.9b	1
✓	30.4b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 2957 to 1427 computations (51.7% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x (.f64 y (.f64 y 4)))
✓	0.0b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	2.7b	(fma.f64 -4 (.f64 y y) (.f64 x x))
	29.8b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series43.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

43.0ms

(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 y (*.f64 y 4))))))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-pow_binary64`
13×	`exp-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

1 → 27

Calls

1 calls:

6.0ms

(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 y (*.f64 y 4))))))

simplify133.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-*l/_binary64`
516×	`fma-neg_binary64`
494×	`associate-*r/_binary64`
371×	`fma-def_binary64`
339×	`associate-/r/_binary64`

Counts

51 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1404
1	198	1310
2	451	1298
3	1457	1280
4	4669	1280
5	4955	1280

prune236.0ms (6.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	174	5	179

Error

0.2b

Counts

179 → 5

Alt Table

Status	Error	Program
✓	30.4b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
▶	30.4b	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.0b	-1
	30.9b	1
✓	30.4b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 5118 to 2630 computations (48.6% saved)

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	0.5b	(expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
	2.7b	(fma.f64 -4 (.f64 y y) (.f64 x x))
	29.8b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series292.0ms (7.5%)

Counts

2 → 48

Calls

2 calls:

254.0ms	(expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
38.0ms	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-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:

1.0ms	(expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
1.0ms	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))

simplify133.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-neg_binary64`
366×	`times-frac_binary64`
335×	`distribute-rgt-neg-in_binary64`
275×	`distribute-neg-frac_binary64`
233×	`associate-/r*_binary64`

Counts

70 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	2052
1	266	1872
2	796	1842
3	3338	1830
4	5047	1830

prune206.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	158	5	163

Error

0.2b

Counts

163 → 5

Alt Table

Status	Error	Program
✓	30.4b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	30.4b	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.0b	-1
▶	30.9b	1
✓	30.4b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 4319 to 2330 computations (46.1% saved)

localize0.0ms (0%)

prune5.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	3	3
Total	5	5

Error

0.2b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	30.4b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	30.4b	(log1p.f64 (expm1.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.0b	-1
✓	30.9b	1
✓	30.4b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 67 to 43 computations (35.8% saved)

regimes425.0ms (10.9%)

Accuracy

Total 14.2b remaining (97.4%)

Threshold costs 0b (0%)

Counts

10 → 6

Compiler

Compiled 788 to 533 computations (32.4% saved)

bsearch155.0ms (4%)

Steps

Iters	Range		Point
5	7.235229896509507e+112	1.660295863337442e+113	1.2394672638586602e+113
10	7.61720174855756e-124	6.728623309684567e-109	1.4444647175745426e-110
9	-4.951806896973363e-139	-3.7714647453367536e-144	-5.632296344258486e-143
9	-4.7365812913246527e-35	-2.033425455470739e-41	-3.889439415150952e-35
9	-8.528289204890226e+106	-6.263126406028741e+99	-7.17550285507751e+99

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`
3×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	90
1	45	90
2	58	90
3	64	90
4	68	90
5	69	90
6	67	90

end2.0ms (0.1%)

Compiler: Compiled 64 to 41 computations (35.9% saved)

sample1.4s (36.2%)

Algorithm

1×

intervals

Results

879.0ms

8000×

body

128

valid

Compiler

Compiled 155 to 99 computations (36.1% saved)

Details

analyze189.0ms (4.9%)

sample44.0ms (1.1%)

simplify127.0ms (3.3%)

prune6.0ms (0.1%)

localize23.0ms (0.6%)

series60.0ms (1.5%)

rewrite13.0ms (0.3%)

simplify173.0ms (4.4%)

prune145.0ms (3.7%)

localize25.0ms (0.6%)

series43.0ms (1.1%)

rewrite12.0ms (0.3%)

simplify133.0ms (3.4%)

prune236.0ms (6.1%)

localize23.0ms (0.6%)

series292.0ms (7.5%)

rewrite3.0ms (0.1%)

simplify133.0ms (3.4%)

prune206.0ms (5.3%)

localize0.0ms (0%)

prune5.0ms (0.1%)

regimes425.0ms (10.9%)

bsearch155.0ms (4%)

simplify10.0ms (0.3%)

end2.0ms (0.1%)

sample1.4s (36.2%)

Profiling