Details

analyze2.0s (37.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
15.6%	84.2%	0.2%	8
15.6%	84.2%	0.2%	9
20.3%	79.5%	0.2%	10
25.3%	74.5%	0.2%	11
34.2%	65.6%	0.2%	12
37.4%	62%	0.6%	13
41.7%	57.7%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
6.0ms	118×	body	128	invalid

Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	2.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	0.2b	(.f64 (.f64 z 3) y)
✓	0.3b	(/.f64 y (*.f64 z 3))
✓	4.9b	(/.f64 t (.f64 (.f64 z 3) y))

series63.0ms (1.1%)

Counts

4 → 132

Calls

4 calls:

29.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
21.0ms	(/.f64 t (.f64 (.f64 z 3) y))
8.0ms	(/.f64 y (*.f64 z 3))
5.0ms	(.f64 (.f64 z 3) y)

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`associate-+l+_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`

Counts

4 → 121

Calls

4 calls:

10.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
6.0ms	(.f64 (.f64 z 3) y)
4.0ms	(/.f64 t (.f64 (.f64 z 3) y))
3.0ms	(/.f64 y (*.f64 z 3))

simplify113.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-def_binary64`
317×	`associate-/l/_binary64`
254×	`distribute-rgt-in_binary64`
243×	`fma-neg_binary64`
235×	`distribute-lft-in_binary64`

Counts

253 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	4171
1	601	3297
2	2065	2964
3	4498	2964
4	4876	2964

prune197.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Error

0.0b

Counts

202 → 8

Alt Table

Status	Error	Program
	2.0b	(+.f64 (-.f64 x (.f64 y (/.f64 1 (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	3.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	2.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	32.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (sqrt.f64 (.f64 (.f64 z 3) y)) (sqrt.f64 (.f64 (.f64 z 3) y)))))
▶	2.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (.f64 y z)))))
	2.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
	2.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 5196 to 3018 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 3 (/.f64 t (*.f64 y z)))
	0.3b	(/.f64 y (*.f64 z 3))
✓	0.6b	(/.f64 1 (/.f64 3 (/.f64 t (*.f64 y z))))
✓	4.9b	(/.f64 t (*.f64 y z))

series55.0ms (1%)

Counts

3 → 72

Calls

3 calls:

20.0ms	(/.f64 1 (/.f64 3 (/.f64 t (*.f64 y z))))
18.0ms	(/.f64 3 (/.f64 t (*.f64 y z)))
18.0ms	(/.f64 t (*.f64 y z))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64`
104×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
51×	`add-exp-log_binary64`

Counts

3 → 211

Calls

3 calls:

8.0ms	(/.f64 1 (/.f64 3 (/.f64 t (*.f64 y z))))
5.0ms	(/.f64 3 (/.f64 t (*.f64 y z)))
3.0ms	(/.f64 t (*.f64 y z))

simplify168.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-/r/_binary64`
633×	`associate-/l*_binary64`
566×	`associate-*l/_binary64`
474×	`associate-l_binary64`
423×	`associate-/l/_binary64`

Counts

283 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	4730
1	408	4289
2	1428	4234
3	4244	4234
4	4634	4234
5	5121	4234

prune389.0ms (7.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	332	1	333
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	334	7	341

Error

Counts

341 → 7

Alt Table

Status	Error	Program
▶	2.0b	(+.f64 (-.f64 x (.f64 y (/.f64 1 (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	3.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	2.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 (/.f64 t y) z))))
✓	2.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (.f64 y z)))))
	2.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 8625 to 4880 computations (43.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (/.f64 1 (.f64 z 3)))
	0.2b	(.f64 (.f64 z 3) y)
✓	0.3b	(/.f64 1 (*.f64 z 3))
	4.9b	(/.f64 t (.f64 (.f64 z 3) y))

series9.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(.f64 y (/.f64 1 (.f64 z 3)))
2.0ms	(/.f64 1 (*.f64 z 3))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`div-exp_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(.f64 y (/.f64 1 (.f64 z 3)))
3.0ms	(/.f64 1 (*.f64 z 3))

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

750×	`associate-/l/_binary64`
529×	`sqr-pow_binary64`
383×	`fma-def_binary64`
321×	`*-commutative_binary64`
319×	`pow-sqr_binary64`

Counts

100 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	829
1	163	656
2	477	655
3	1661	655
4	1885	655
5	2096	655
6	2529	655
7	3087	655
8	3663	655
9	5126	655

prune162.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	159	7	166

Error

Counts

166 → 7

Alt Table

Status	Error	Program
✓	2.0b	(+.f64 (-.f64 x (.f64 y (/.f64 1 (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	3.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
▶	2.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 (/.f64 t y) z))))
✓	2.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (.f64 y z)))))
	2.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 3650 to 2373 computations (35% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	0.2b	(.f64 (.f64 z 3) y)
✓	0.3b	(*.f64 (/.f64 1 z) (/.f64 y 3))
	4.9b	(/.f64 t (.f64 (.f64 z 3) y))

series36.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
7.0ms	(*.f64 (/.f64 1 z) (/.f64 y 3))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`add-exp-log_binary64`
22×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 84

Calls

2 calls:

9.0ms	(*.f64 (/.f64 1 z) (/.f64 y 3))
7.0ms	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

395×	`associate-/l*_binary64`
340×	`fma-def_binary64`
338×	`times-frac_binary64`
273×	`associate-/r*_binary64`
245×	`distribute-rgt-in_binary64`

Counts

156 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2431
1	482	2180
2	1550	2054
3	4450	2054
4	5041	2054

prune194.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
✓	2.0b	(+.f64 (-.f64 x (.f64 y (/.f64 1 (.f64 z 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	3.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
✓	2.0b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.0b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 (/.f64 t y) z))))
✓	2.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (.f64 y z)))))
	2.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 5216 to 3271 computations (37.3% saved)

regimes375.0ms (6.8%)

Accuracy

Total 0.4b remaining (95.5%)

Threshold costs 0.4b (95.5%)

Counts

41 → 3

Compiler

Compiled 4762 to 3297 computations (30.8% saved)

bsearch47.0ms (0.9%)

Steps

Iters	Range		Point
8	88128836270984.0	33193977433672370.0	189002726950466.9
8	-7.417400173421259e-58	-1.0505916886165403e-61	-8.62393080127238e-60

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	70
1	43	70
2	60	70
3	73	70
4	82	70
5	85	70
6	85	70

end3.0ms (0.1%)

Compiler: Compiled 52 to 33 computations (36.5% saved)

sample1.2s (21.4%)

Algorithm

1×

intervals

Results

471.0ms	8000×	body	128	valid
189.0ms	3162×	body	128	invalid

Compiler

Compiled 212 to 146 computations (31.1% saved)

Details

analyze2.0s (37.1%)

sample38.0ms (0.7%)

simplify93.0ms (1.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series63.0ms (1.1%)

rewrite32.0ms (0.6%)

simplify113.0ms (2.1%)

prune197.0ms (3.6%)

localize12.0ms (0.2%)

series55.0ms (1%)

rewrite34.0ms (0.6%)

simplify168.0ms (3.1%)

prune389.0ms (7.1%)

localize11.0ms (0.2%)

series9.0ms (0.2%)

rewrite12.0ms (0.2%)

simplify99.0ms (1.8%)

prune162.0ms (3%)

localize11.0ms (0.2%)

series36.0ms (0.7%)

rewrite21.0ms (0.4%)

simplify89.0ms (1.6%)

prune194.0ms (3.5%)

regimes375.0ms (6.8%)

bsearch47.0ms (0.9%)

simplify5.0ms (0.1%)

end3.0ms (0.1%)

sample1.2s (21.4%)

Profiling