Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.6s (34.3%)

Results

647.0ms	2069×	body	1024	valid
414.0ms	4385×	body	128	valid
249.0ms	1043×	body	512	valid
108.0ms	251×	body	2048	valid
85.0ms	508×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	1.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite224.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))

simplify1.0s (21.6%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 619

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune705.0ms (15%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	615	4	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	616	4	620

Error

0.0b

Counts

620 → 4

Alt Table

Status	Error	Program
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
▶	29.4b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
	61.1b	(+.f64 (fma.f64 1 (/.f64 x (+.f64 x 1)) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
	31.3b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 30508 to 22481 computations (26.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 x) (-.f64 -1 x))
✓	0.0b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
✓	29.5b	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))
3.0ms	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
2.0ms	(*.f64 (+.f64 1 x) (-.f64 -1 x))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 96

Calls

3 calls:

7.0ms	(*.f64 (+.f64 1 x) (-.f64 -1 x))
2.0ms	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
0.0ms	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Rules

795×	`distribute-rgt-in_binary64`
696×	`distribute-lft-in_binary64`
603×	`fma-neg_binary64`
160×	`associate-l_binary64`
149×	`associate-r_binary64`

Counts

132 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2768
1	465	2474
2	1647	2284
3	4716	2272
4	4988	2272

prune108.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	166	3	169

Error

0.0b

Counts

169 → 3

Alt Table

Status	Error	Program
▶	14.2b	(/.f64 (neg.f64 (+.f64 1 (*.f64 3 x))) (fma.f64 x x -1))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	31.3b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 4601 to 3003 computations (34.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 3 x))
✓	14.2b	(/.f64 (neg.f64 (+.f64 1 (*.f64 3 x))) (fma.f64 x x -1))

series5.0ms (0.1%)

Counts

2 → 15

Calls

2 calls:

4.0ms	(/.f64 (neg.f64 (+.f64 1 (*.f64 3 x))) (fma.f64 x x -1))
1.0ms	(+.f64 1 (*.f64 3 x))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
12×	`distribute-lft-neg-in_binary64`

Counts

2 → 77

Calls

2 calls:

4.0ms	(/.f64 (neg.f64 (+.f64 1 (*.f64 3 x))) (fma.f64 x x -1))
2.0ms	(+.f64 1 (*.f64 3 x))

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

844×	`div-sub_binary64`
370×	`fma-neg_binary64`
350×	`times-frac_binary64`
346×	`fma-def_binary64`
279×	`associate-l_binary64`

Counts

92 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2071
1	346	1769
2	1077	1671
3	3782	1671
4	5788	1671

prune115.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	143	4	147

Error

Counts

147 → 4

Alt Table

Status	Error	Program
✓	14.2b	(/.f64 (neg.f64 (+.f64 1 (*.f64 3 x))) (fma.f64 x x -1))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	21.5b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))) (sqrt.f64 (/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))))
▶	14.3b	(.f64 (neg.f64 (+.f64 1 (.f64 3 x))) (/.f64 1 (fma.f64 x x -1)))

Compiler

Compiled 2973 to 2269 computations (23.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (*.f64 3 x))
✓	0.3b	(/.f64 1 (fma.f64 x x -1))
✓	13.9b	(.f64 (neg.f64 (+.f64 1 (.f64 3 x))) (/.f64 1 (fma.f64 x x -1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1 (fma.f64 x x -1))
3.0ms	(.f64 (neg.f64 (+.f64 1 (.f64 3 x))) (/.f64 1 (fma.f64 x x -1)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 83

Calls

2 calls:

9.0ms	(.f64 (neg.f64 (+.f64 1 (.f64 3 x))) (/.f64 1 (fma.f64 x x -1)))
2.0ms	(/.f64 1 (fma.f64 x x -1))

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-neg_binary64`
386×	`distribute-rgt-in_binary64`
364×	`fma-def_binary64`
343×	`distribute-lft-in_binary64`
338×	`div-sub_binary64`

Counts

107 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1910
1	391	1605
2	1270	1506
3	3782	1502
4	4974	1502
5	5069	1502

prune123.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	174	3	177

Error

Counts

177 → 3

Alt Table

Status	Error	Program
	21.6b	(/.f64 (fma.f64 x (.f64 x 9) -1) (.f64 (fma.f64 x x -1) (fma.f64 x -3 1)))
	32.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
✓	14.3b	(.f64 (neg.f64 (+.f64 1 (.f64 3 x))) (/.f64 1 (fma.f64 x x -1)))

Compiler

Compiled 3380 to 2646 computations (21.7% saved)

regimes254.0ms (5.4%)

Accuracy

Total 0.0b remaining (68.3%)

Threshold costs 0.0b (68.3%)

Counts

100 → 3

Compiler

Compiled 3574 to 2730 computations (23.6% saved)

bsearch7.0ms (0.1%)

Steps

Iters	Range		Point
1	41160245.32747433	1.6903888093339274e+24	8162611635593491.0
1	-264437911551.847	-16603.855853596455	-66059582.89406409

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	90
1	45	88
2	70	88
3	89	88
4	99	88
5	102	88
6	99	88

end84.0ms (1.8%)

Compiler: Compiled 175 to 130 computations (25.7% saved)

Details

analyze5.0ms (0.1%)

sample1.6s (34.3%)

simplify85.0ms (1.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite224.0ms (4.8%)

simplify1.0s (21.6%)

prune705.0ms (15%)

localize9.0ms (0.2%)

series9.0ms (0.2%)

rewrite17.0ms (0.4%)

simplify93.0ms (2%)

prune108.0ms (2.3%)

localize6.0ms (0.1%)

series5.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify78.0ms (1.7%)

prune115.0ms (2.4%)

localize8.0ms (0.2%)

series6.0ms (0.1%)

rewrite16.0ms (0.3%)

simplify89.0ms (1.9%)

prune123.0ms (2.6%)

regimes254.0ms (5.4%)

bsearch7.0ms (0.1%)

simplify4.0ms (0.1%)

end84.0ms (1.8%)

Profiling