Details

analyze892.0ms (11.2%)

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)

sample2.5s (31%)

Results

1.8s	8256×	body	128	valid
537.0ms	2910×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify75.0ms (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

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

13.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.8b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	30.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize9.0ms (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))
✓	1.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	13.6b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series91.0ms (1.1%)

Counts

4 → 132

Calls

4 calls:

36.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
24.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
24.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite73.0ms (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:

18.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
13.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
5.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
4.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify193.0ms (2.4%)

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

prune240.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	355	6	361
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	357	6	363

Error

0.2b

Counts

363 → 6

Alt Table

Status	Error	Program
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
	14.1b	(.f64 -1/2 (fma.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x)))) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) y) (neg.f64 y)))
	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	13.8b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
	33.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
▶	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))

Compiler

Compiled 10954 to 2533 computations (76.9% saved)

localize12.0ms (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)))

series57.0ms (0.7%)

Counts

3 → 100

Calls

3 calls:

28.0ms	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
19.0ms	(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:

5.0ms	(/.f64 (-.f64 z x) y)
3.0ms	(*.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))

simplify107.0ms (1.3%)

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

prune87.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Error

0.2b

Counts

134 → 5

Alt Table

Status	Error	Program
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
▶	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	1.0b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 y))) (neg.f64 y)))
	13.8b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
✓	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))

Compiler

Compiled 2721 to 1050 computations (61.4% 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))
✓	0.2b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series93.0ms (1.2%)

Counts

4 → 132

Calls

4 calls:

33.0ms	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
26.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
20.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
14.0ms	(/.f64 y (-.f64 z x))

rewrite359.0ms (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:

43.0ms	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
34.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
9.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
4.0ms	(/.f64 y (-.f64 z x))

simplify898.0ms (11.3%)

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

prune625.0ms (7.9%)

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
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
✓	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
▶	1.0b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 y))) (neg.f64 y)))
	13.8b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
✓	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))

Compiler

Compiled 38387 to 8394 computations (78.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
✓	0.5b	(cbrt.f64 y)
✓	0.6b	(cbrt.f64 (-.f64 z x))

series125.0ms (1.6%)

Counts

4 → 72

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
34.0ms	(cbrt.f64 y)
31.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
22.0ms	(cbrt.f64 (-.f64 z x))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`cbrt-prod_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`

Counts

4 → 130

Calls

4 calls:

9.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
2.0ms	(cbrt.f64 (-.f64 z x))
1.0ms	(cbrt.f64 y)

simplify146.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
574×	`cancel-sign-sub-inv_binary64`
314×	`unswap-sqr_binary64`
273×	`associate-r_binary64`
214×	`fma-neg_binary64`

Counts

202 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	3700
1	705	3504
2	2312	3344
3	4777	3307
4	4984	3307
5	4943	3307

prune301.0ms (3.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	365	5	370

Error

0.2b

Counts

370 → 5

Alt Table

Status	Error	Program
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
✓	0.4b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	1.0b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 y))) (neg.f64 y)))
	13.8b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
✓	0.3b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))

Compiler

Compiled 16243 to 5874 computations (63.8% saved)

regimes953.0ms (12%)

Accuracy

Total 0.1b remaining (56.7%)

Threshold costs 0.1b (56.7%)

Counts

148 → 1

Compiler

Compiled 23250 to 13422 computations (42.3% saved)

simplify2.0ms (0%)

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	13	19
1	22	19
2	27	19
3	30	19
4	31	19
5	30	19

end78.0ms (1%)

Compiler: Compiled 132 to 81 computations (38.6% saved)

Details

analyze892.0ms (11.2%)

sample2.5s (31%)

simplify75.0ms (0.9%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series91.0ms (1.1%)

rewrite73.0ms (0.9%)

simplify193.0ms (2.4%)

prune240.0ms (3%)

localize12.0ms (0.1%)

series57.0ms (0.7%)

rewrite12.0ms (0.2%)

simplify107.0ms (1.3%)

prune87.0ms (1.1%)

localize8.0ms (0.1%)

series93.0ms (1.2%)

rewrite359.0ms (4.5%)

simplify898.0ms (11.3%)

prune625.0ms (7.9%)

localize19.0ms (0.2%)

series125.0ms (1.6%)

rewrite26.0ms (0.3%)

simplify146.0ms (1.8%)

prune301.0ms (3.8%)

regimes953.0ms (12%)

simplify2.0ms (0%)

end78.0ms (1%)

Profiling