Details

analyze119.0ms (2.8%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample840.0ms (19.6%)

Infinites

41.9% of outputs are infinite.

Results

736.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify79.0ms (1.9%)

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

11.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.5b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	18.5b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.3b	(-.f64 (.f64 z z) (.f64 x x))
✓	9.2b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series32.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

26.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
6.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
5×	`difference-of-squares_binary64`

Counts

2 → 53

Calls

2 calls:

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

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Rules

302×	`fma-neg_binary64`
251×	`div-sub_binary64`
208×	`associate-l_binary64`
194×	`unswap-sqr_binary64`
188×	`distribute-rgt-neg-out_binary64`

Counts

113 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	1690
1	254	1582
2	705	1576
3	2757	1576
4	4564	1576
5	4907	1576

prune83.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Error

Counts

91 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	30.3b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (sqrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	0.4b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
▶	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	11.5b	(.f64 -1/2 (-.f64 (.f64 (-.f64 (.f64 z z) (.f64 x x)) (/.f64 1 y)) y))

Compiler

Compiled 2019 to 699 computations (65.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) y)
✓	0.1b	(*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))

series35.0ms (0.8%)

Counts

2 → 64

Calls

2 calls:

21.0ms	(*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))
14.0ms	(/.f64 (-.f64 z x) y)

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

2 → 87

Calls

2 calls:

9.0ms	(*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))
6.0ms	(/.f64 (-.f64 z x) y)

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
705×	`div-sub_binary64`
517×	`associate-*l/_binary64`
373×	`associate-*r/_binary64`
326×	`associate-/l*_binary64`

Counts

151 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	154	2063
1	494	1947
2	1389	1947
3	3596	1947
4	5792	1947

prune112.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	128	5	133

Error

Counts

133 → 5

Alt Table

Status	Error	Program
	12.8b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (/.f64 (-.f64 z x) y) (-.f64 (.f64 x x) (.f64 z z))) (-.f64 x z)) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	0.4b	(.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 z x) (/.f64 y (-.f64 z x))) y))
	0.3b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) 1) (.f64 (/.f64 (cbrt.f64 (-.f64 z x)) y) (+.f64 x z))) y))

Compiler

Compiled 2821 to 931 computations (67% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series37.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

22.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
15.0ms	(/.f64 y (-.f64 z x))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`times-frac_binary64`
161×	`*-un-lft-identity_binary64`
117×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 167

Calls

2 calls:

11.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
4.0ms	(/.f64 y (-.f64 z x))

simplify142.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

498×	`times-frac_binary64`
445×	`distribute-rgt-in_binary64`
422×	`fma-def_binary64`
405×	`distribute-lft-in_binary64`
203×	`associate-/r/_binary64`

Counts

227 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	5160
1	618	5010
2	2216	4849
3	4785	4849
4	4987	4849

prune181.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	241	5	246

Error

Counts

246 → 5

Alt Table

Status	Error	Program
	12.8b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (/.f64 (-.f64 z x) y) (-.f64 (.f64 x x) (.f64 z z))) (-.f64 x z)) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	0.4b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
▶	0.3b	(.f64 -1/2 (-.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

Compiler

Compiled 6038 to 1757 computations (70.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x))))
✓	0.2b	(/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z)))
✓	0.5b	(cbrt.f64 (+.f64 x z))

series369.0ms (8.6%)

Counts

4 → 120

Calls

4 calls:

298.0ms	(/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))
31.0ms	(*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z)))
21.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x))))
19.0ms	(cbrt.f64 (+.f64 x z))

rewrite400.0ms (9.3%)

Algorithm

1×	rewrite-expression-head

Rules

525×	`times-frac_binary64`
427×	`*-un-lft-identity_binary64`
344×	`add-sqr-sqrt_binary64`
235×	`add-cube-cbrt_binary64`
202×	`cbrt-prod_binary64`

Counts

4 → 464

Calls

4 calls:

209.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x))))
79.0ms	(*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z)))
9.0ms	(/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))
2.0ms	(cbrt.f64 (+.f64 x z))

simplify348.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-/l*_binary64`
433×	`fma-def_binary64`
351×	`associate-/r/_binary64`
257×	`associate-/l/_binary64`
211×	`*-commutative_binary64`

Counts

584 → 737

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	694	17897
1	1897	15839
2	4843	15837
3	5079	15837

prune751.0ms (17.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	849	0	849
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	849	5	854

Error

Counts

854 → 5

Alt Table

Status	Error	Program
	12.8b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (/.f64 (-.f64 z x) y) (-.f64 (.f64 x x) (.f64 z z))) (-.f64 x z)) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	0.4b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
✓	0.3b	(.f64 -1/2 (-.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

Compiler

Compiled 32772 to 9342 computations (71.5% saved)

regimes395.0ms (9.2%)

Accuracy

Total 0.1b remaining (70.1%)

Threshold costs 0.1b (70.1%)

Counts

58 → 1

Compiler

Compiled 8654 to 4847 computations (44% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	17	19
2	25	19
3	29	19
4	31	19
5	31	19

end84.0ms (2%)

Compiler: Compiled 138 to 80 computations (42% saved)

Details

analyze119.0ms (2.8%)

sample840.0ms (19.6%)

simplify79.0ms (1.9%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series32.0ms (0.8%)

rewrite12.0ms (0.3%)

simplify84.0ms (2%)

prune83.0ms (1.9%)

localize8.0ms (0.2%)

series35.0ms (0.8%)

rewrite20.0ms (0.5%)

simplify79.0ms (1.8%)

prune112.0ms (2.6%)

localize8.0ms (0.2%)

series37.0ms (0.9%)

rewrite32.0ms (0.7%)

simplify142.0ms (3.3%)

prune181.0ms (4.2%)

localize13.0ms (0.3%)

series369.0ms (8.6%)

rewrite400.0ms (9.3%)

simplify348.0ms (8.1%)

prune751.0ms (17.5%)

regimes395.0ms (9.2%)

simplify3.0ms (0.1%)

end84.0ms (2%)

Profiling