Details

analyze18.0ms (0.9%)

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)

sample1.2s (56%)

Results

993.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify123.0ms (6%)

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

prune3.0ms (0.2%)

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

31.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.8b	(/.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)

localize11.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.8b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	31.2b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series31.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
9.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
1.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

simplify89.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
491×	`div-sub_binary64`
392×	`fma-neg_binary64`
350×	`cancel-sign-sub-inv_binary64`
219×	`distribute-rgt-in_binary64`

Counts

87 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	2105
1	216	1928
2	563	1916
3	2054	1898
4	4435	1862
5	5400	1862

prune58.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Error

0.4b

Counts

91 → 4

Alt Table

Status	Error	Program
	31.8b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.6b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	32.7b	-1
▶	30.9b	1

Compiler

Compiled 2461 to 1241 computations (49.6% saved)

localize0.0ms (0%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

0.4b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	31.8b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.6b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	32.7b	-1
✓	30.9b	1

Compiler

Compiled 75 to 51 computations (32% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	1.3b	(log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
	3.8b	(fma.f64 -4 (.f64 y y) (.f64 x x))
	31.2b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series74.0ms (3.6%)

Counts

2 → 48

Calls

2 calls:

51.0ms	(log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
23.0ms	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))

rewrite2.0ms (0.1%)

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 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))

simplify106.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-neg_binary64`
285×	`sub-neg_binary64`
276×	`distribute-rgt-neg-in_binary64`
266×	`distribute-lft-neg-in_binary64`
247×	`distribute-neg-frac_binary64`

Counts

70 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	2015
1	299	1867
2	811	1815
3	3036	1801
4	4958	1801
5	5079	1801

prune112.0ms (5.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Error

0.4b

Counts

173 → 4

Alt Table

Status	Error	Program
✓	31.8b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.6b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	32.7b	-1
✓	30.9b	1

Compiler

Compiled 4627 to 2563 computations (44.6% saved)

localize0.0ms (0%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.4b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	31.8b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.6b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	32.7b	-1
✓	30.9b	1

Compiler

Compiled 39 to 27 computations (30.8% saved)

regimes135.0ms (6.5%)

Accuracy

Total 13.9b remaining (97.7%)

Threshold costs 0b (0%)

Counts

8 → 4

Compiler

Compiled 862 to 590 computations (31.6% saved)

bsearch37.0ms (1.8%)

Steps

Iters	Range	Point
9	3.4032379551473655e+152	2.0790466465220898e+160	4.308904655747995e+153
8	5.670866588851173e-97	2.1689855373008987e-93	1.0915839863199315e-96
0	-1.6570329713057493e+28	-1.6533770502747204e+28	-1.655205010790235e+28

Iters

Range

Point

3.4032379551473655e+152

2.0790466465220898e+160

4.308904655747995e+153

5.670866588851173e-97

2.1689855373008987e-93

1.0915839863199315e-96

-1.6570329713057493e+28

-1.6533770502747204e+28

-1.655205010790235e+28

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	49
1	30	49
2	29	49

end68.0ms (3.3%)

Compiler: Compiled 111 to 77 computations (30.6% saved)

Details

analyze18.0ms (0.9%)

sample1.2s (56%)

simplify123.0ms (6%)

prune3.0ms (0.2%)

localize11.0ms (0.5%)

series31.0ms (1.5%)

rewrite8.0ms (0.4%)

simplify89.0ms (4.3%)

prune58.0ms (2.8%)

localize0.0ms (0%)

prune3.0ms (0.1%)

localize12.0ms (0.6%)

series74.0ms (3.6%)

rewrite2.0ms (0.1%)

simplify106.0ms (5.2%)

prune112.0ms (5.4%)

localize0.0ms (0%)

prune2.0ms (0.1%)

regimes135.0ms (6.5%)

bsearch37.0ms (1.8%)

simplify13.0ms (0.6%)

end68.0ms (3.3%)

Profiling