Details

analyze1.2s (22.6%)

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)

sample1.4s (26.1%)

Results

979.0ms	8256×	body	128	valid
352.0ms	3053×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify74.0ms (1.4%)

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 (0.1%)

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

9.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.8b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	24.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	9.7b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series69.0ms (1.3%)

Counts

3 → 96

Calls

3 calls:

33.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
29.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
61×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64`
49×	`prod-diff_binary64`

Counts

3 → 137

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
4.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
2.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify124.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
355×	`distribute-rgt-in_binary64`
349×	`distribute-lft-in_binary64`
265×	`fma-neg_binary64`
183×	`exp-prod_binary64`

Counts

233 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4494
1	395	4071
2	1546	3650
3	4392	3650
4	4970	3650

prune124.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	193	5	198

Error

0.0b

Counts

198 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
▶	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	24.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	9.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))

Compiler

Compiled 5233 to 1300 computations (75.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series72.0ms (1.3%)

Counts

3 → 100

Calls

3 calls:

30.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
27.0ms	(-.f64 (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)
15.0ms	(/.f64 (-.f64 z x) y)

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

13.0ms	(-.f64 (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)
8.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
4.0ms	(/.f64 (-.f64 z x) y)

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-/l*_binary64`
645×	`fma-def_binary64`
220×	`fma-neg_binary64`
213×	`associate-/l/_binary64`
160×	`associate-l_binary64`

Counts

205 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	2969
1	460	2808
2	2080	2785
3	4757	2785
4	4973	2785

prune111.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	164	5	169

Error

0.0b

Counts

169 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	24.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	9.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))

Compiler

Compiled 3546 to 1103 computations (68.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 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 (+.f64 z x) (/.f64 y (-.f64 z x)))

series69.0ms (1.3%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
22.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
20.0ms	(/.f64 y (-.f64 z x))

rewrite146.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

753×	`times-frac_binary64`
750×	`*-un-lft-identity_binary64`
545×	`add-sqr-sqrt_binary64`
402×	`add-cube-cbrt_binary64`
267×	`prod-diff_binary64`

Counts

3 → 543

Calls

3 calls:

34.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
11.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
3.0ms	(/.f64 y (-.f64 z x))

simplify418.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

361×	`fma-neg_binary64`
213×	`associate-*l/_binary64`
202×	`associate-/l*_binary64`
199×	`associate-/r/_binary64`
183×	`*-commutative_binary64`

Counts

639 → 561

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	17494
1	881	16388
2	3922	15169
3	4593	15169
4	4939	15169

prune328.0ms (6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	559	2	561
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	560	6	566

Error

Counts

566 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	24.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
▶	0.7b	(.f64 -1/2 (+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (+.f64 x z) (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 z x)))) (neg.f64 y)) 0))
	13.0b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z x)) 3))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	9.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))

Compiler

Compiled 18118 to 4031 computations (77.8% saved)

localize17.0ms (0.3%)

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)))
✓	0.6b	(cbrt.f64 (-.f64 z x))
✓	0.6b	(cbrt.f64 y)

series141.0ms (2.6%)

Counts

4 → 72

Calls

4 calls:

38.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
37.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
36.0ms	(cbrt.f64 y)
30.0ms	(cbrt.f64 (-.f64 z x))

rewrite28.0ms (0.5%)

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:

10.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
9.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
2.0ms	(cbrt.f64 (-.f64 z x))
1.0ms	(cbrt.f64 y)

simplify144.0ms (2.6%)

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

prune343.0ms (6.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	365	6	371

Error

Counts

371 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	24.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
✓	0.7b	(.f64 -1/2 (+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (+.f64 x z) (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 z x)))) (neg.f64 y)) 0))
	13.0b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z x)) 3))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	9.8b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))

Compiler

Compiled 16266 to 5585 computations (65.7% saved)

regimes329.0ms (6%)

Accuracy

Total 0.1b remaining (78.2%)

Threshold costs 0.1b (78.2%)

Counts

53 → 1

Compiler

Compiled 7582 to 4533 computations (40.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`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	18	19
2	26	19
3	30	19
4	32	19
5	32	19

end84.0ms (1.5%)

Compiler: Compiled 155 to 94 computations (39.4% saved)

Details

analyze1.2s (22.6%)

sample1.4s (26.1%)

simplify74.0ms (1.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series69.0ms (1.3%)

rewrite30.0ms (0.5%)

simplify124.0ms (2.3%)

prune124.0ms (2.3%)

localize7.0ms (0.1%)

series72.0ms (1.3%)

rewrite32.0ms (0.6%)

simplify107.0ms (2%)

prune111.0ms (2%)

localize7.0ms (0.1%)

series69.0ms (1.3%)

rewrite146.0ms (2.7%)

simplify418.0ms (7.6%)

prune328.0ms (6%)

localize17.0ms (0.3%)

series141.0ms (2.6%)

rewrite28.0ms (0.5%)

simplify144.0ms (2.6%)

prune343.0ms (6.2%)

regimes329.0ms (6%)

simplify3.0ms (0%)

end84.0ms (1.5%)

Profiling