Details

analyze1.1s (14.1%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (19.3%)

Results

1.0s	8256×	body	128	valid
344.0ms	2880×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
795×	`div-sub_binary64`
536×	`times-frac_binary64`
518×	`neg-mul-1_binary64`
376×	`distribute-frac-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	65	20
3	126	20
4	278	20
5	602	20
6	1317	19
7	2853	19
8	4446	19
9	4743	19
10	4991	19

prune3.0ms (0%)

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

14.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.0b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 63 to 36 computations (42.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
✓	0.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	13.9b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series106.0ms (1.4%)

Counts

4 → 132

Calls

4 calls:

40.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
31.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
28.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-sqr-sqrt_binary64`
150×	`*-un-lft-identity_binary64`
146×	`add-cube-cbrt_binary64`
145×	`prod-diff_binary64`
134×	`times-frac_binary64`

Counts

4 → 266

Calls

4 calls:

11.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
10.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
9.0ms	(-.f64 (.f64 z z) (.f64 x x))
4.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

simplify177.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

529×	`distribute-rgt-in_binary64`
508×	`distribute-lft-in_binary64`
204×	`fma-neg_binary64`
182×	`cancel-sign-sub-inv_binary64`
156×	`*-commutative_binary64`

Counts

398 → 361

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	9611
1	543	8693
2	1996	7471
3	4966	7471

prune215.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	356	5	361
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	357	5	362

Error

0.2b

Counts

362 → 5

Alt Table

Status	Error	Program
	32.3b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	54.2b	(*.f64 1/2 (/.f64 (pow.f64 x 2) y))
	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
▶	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	14.0b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))

Compiler

Compiled 10876 to 2501 computations (77% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) y)
✓	0.1b	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))
✓	0.2b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))

series62.0ms (0.8%)

Counts

3 → 100

Calls

3 calls:

32.0ms	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
20.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))
9.0ms	(/.f64 (-.f64 z x) y)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

4.0ms	(/.f64 (-.f64 z x) y)
4.0ms	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
0.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

305×	`distribute-rgt-in_binary64`
305×	`fma-neg_binary64`
298×	`distribute-lft-in_binary64`
259×	`div-sub_binary64`
234×	`distribute-rgt-neg-out_binary64`

Counts

172 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	2896
1	323	2597
2	754	2597
3	2602	2570
4	4422	2570
5	4969	2570

prune76.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	128	5	133

Error

0.2b

Counts

133 → 5

Alt Table

Status	Error	Program
	32.3b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	14.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (neg.f64 (/.f64 x y)) (neg.f64 y)))
▶	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	14.0b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))

Compiler

Compiled 2699 to 1044 computations (61.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
✓	0.0b	(/.f64 y (-.f64 z x))
✓	0.2b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.3b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series104.0ms (1.4%)

Counts

4 → 132

Calls

4 calls:

39.0ms	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
27.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
22.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
16.0ms	(/.f64 y (-.f64 z x))

rewrite336.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

1679×	`*-un-lft-identity_binary64`
1620×	`times-frac_binary64`
1231×	`add-sqr-sqrt_binary64`
933×	`add-cube-cbrt_binary64`
801×	`prod-diff_binary64`

Counts

4 → 1111

Calls

4 calls:

38.0ms	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
29.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
9.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
5.0ms	(/.f64 y (-.f64 z x))

simplify1.2s (15.5%)

Algorithm

1×	egg-herbie

Rules

413×	`*-commutative_binary64`
315×	`fma-neg_binary64`
224×	`associate-*l/_binary64`
207×	`associate-/l*_binary64`
205×	`associate-/r/_binary64`

Counts

1243 → 1034

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	867	45165
1	1115	42675
2	4631	42675
3	5014	42675

prune730.0ms (9.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1034	0	1034
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1034	5	1039

Error

0.2b

Counts

1039 → 5

Alt Table

Status	Error	Program
	32.3b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	14.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (neg.f64 (/.f64 x y)) (neg.f64 y)))
✓	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
▶	14.0b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))

Compiler

Compiled 38365 to 8388 computations (78.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
✓	0.3b	(/.f64 1 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))))
	0.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	14.1b	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))

series132.0ms (1.8%)

Counts

3 → 108

Calls

3 calls:

66.0ms	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))
38.0ms	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
28.0ms	(/.f64 1 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))))

rewrite183.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

660×	`times-frac_binary64`
459×	`add-sqr-sqrt_binary64`
448×	`*-un-lft-identity_binary64`
443×	`add-cube-cbrt_binary64`
354×	`prod-diff_binary64`

Counts

3 → 524

Calls

3 calls:

53.0ms	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
6.0ms	(/.f64 1 (/.f64 y (-.f64 (.f64 z z) (.f64 x x))))
4.0ms	(/.f64 y (-.f64 (.f64 z z) (.f64 x x)))

simplify432.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-in_binary64`
211×	`times-frac_binary64`
189×	`*-commutative_binary64`
186×	`fma-neg_binary64`
179×	`cancel-sign-sub-inv_binary64`

Counts

632 → 628

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	450	21934
1	676	19782
2	2828	17079
3	5175	17079

prune483.0ms (6.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	656	0	656
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	656	5	661

Error

0.2b

Counts

661 → 5

Alt Table

Status	Error	Program
	32.3b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	14.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (neg.f64 (/.f64 x y)) (neg.f64 y)))
✓	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
✓	14.0b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))

Compiler

Compiled 25354 to 8253 computations (67.4% saved)

regimes441.0ms (5.9%)

Accuracy

Total 0.1b remaining (60.5%)

Threshold costs 0.1b (60.5%)

Counts

66 → 1

Compiler

Compiled 8085 to 4950 computations (38.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	19	19
2	24	19
3	27	19
4	28	19
5	28	19

end76.0ms (1%)

Compiler: Compiled 121 to 78 computations (35.5% saved)

Details

analyze1.1s (14.1%)

sample1.5s (19.3%)

simplify71.0ms (0.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series106.0ms (1.4%)

rewrite67.0ms (0.9%)

simplify177.0ms (2.3%)

prune215.0ms (2.9%)

localize10.0ms (0.1%)

series62.0ms (0.8%)

rewrite12.0ms (0.2%)

simplify102.0ms (1.4%)

prune76.0ms (1%)

localize8.0ms (0.1%)

series104.0ms (1.4%)

rewrite336.0ms (4.5%)

simplify1.2s (15.5%)

prune730.0ms (9.7%)

localize9.0ms (0.1%)

series132.0ms (1.8%)

rewrite183.0ms (2.4%)

simplify432.0ms (5.7%)

prune483.0ms (6.4%)

regimes441.0ms (5.9%)

simplify4.0ms (0.1%)

end76.0ms (1%)

Profiling