Details

analyze184.0ms (3.8%)

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
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.5%	34.3%	0.1%	8
65.5%	34.3%	0.1%	9
76.5%	23.4%	0.1%	10
81.9%	17.9%	0.1%	11
81.9%	17.9%	0.1%	12
87.8%	12.1%	0.1%	13
90.7%	9.2%	0.1%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample989.0ms (20.4%)

Infinites

3.5% of outputs are infinite.

Results

871.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.2b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series101.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

78.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
18.0ms	(/.f64 v (+.f64 t1 u))
5.0ms	(-.f64 -1 (/.f64 u t1))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
229×	`add-sqr-sqrt_binary64`
219×	`*-un-lft-identity_binary64`
129×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`

Counts

3 → 257

Calls

3 calls:

13.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
7.0ms	(-.f64 -1 (/.f64 u t1))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify223.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
310×	`associate-/l/_binary64`
233×	`associate-/l*_binary64`
223×	`div-sub_binary64`
212×	`fma-neg_binary64`

Counts

341 → 303

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	465	9966
1	1202	8417
2	3569	8323
3	4946	8323
4	5008	8323

prune298.0ms (6.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	298	5	303
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	299	6	305

Error

Counts

305 → 6

Alt Table

Status	Error	Program
	16.2b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	2.2b	(.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
▶	1.9b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	12.4b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
	3.4b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))

Compiler

Compiled 8148 to 2911 computations (64.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.5b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	1.7b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series88.0ms (1.8%)

Counts

2 → 60

Calls

2 calls:

78.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
10.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`

Counts

2 → 122

Calls

2 calls:

18.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
8.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

simplify114.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
478×	`associate-*l/_binary64`
442×	`associate-/r*_binary64`
294×	`fma-neg_binary64`
258×	`fma-def_binary64`

Counts

182 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	3921
1	576	3621
2	1776	3532
3	4978	3523
4	5138	3523

prune342.0ms (7.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	332	2	334
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	334	6	340

Error

Counts

340 → 6

Alt Table

Status	Error	Program
✓	1.9b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	16.2b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	12.4b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
▶	1.5b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
	3.4b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))

Compiler

Compiled 8497 to 3597 computations (57.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
✓	1.0b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
✓	3.1b	(/.f64 v (-.f64 -1 (/.f64 u t1)))

series102.0ms (2.1%)

Counts

2 → 72

Calls

2 calls:

73.0ms	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
29.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
183×	`add-sqr-sqrt_binary64`
176×	`*-un-lft-identity_binary64`
88×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

13.0ms	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
6.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))

simplify187.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

779×	`associate-/l*_binary64`
346×	`fma-def_binary64`
316×	`associate-/r/_binary64`
291×	`fma-neg_binary64`
283×	`associate-/l/_binary64`

Counts

258 → 282

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	7376
1	823	7177
2	2373	7080
3	4873	7080
4	5034	7080

prune572.0ms (11.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	365	6	371

Error

Counts

371 → 6

Alt Table

Status	Error	Program
✓	1.9b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
▶	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	16.2b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	12.4b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
✓	1.5b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
	3.4b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))

Compiler

Compiled 9737 to 3862 computations (60.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.2b	(*.f64 (neg.f64 u) (/.f64 1 t1))
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))

series107.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

85.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
18.0ms	(*.f64 (neg.f64 u) (/.f64 1 t1))
5.0ms	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`times-frac_binary64`
90×	`*-un-lft-identity_binary64`
72×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
18×	`associate-/l*_binary64`

Counts

3 → 157

Calls

3 calls:

9.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
8.0ms	(*.f64 (neg.f64 u) (/.f64 1 t1))
3.0ms	(+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1)))

simplify274.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
214×	`div-sub_binary64`
200×	`distribute-rgt-neg-out_binary64`
191×	`distribute-lft-neg-out_binary64`
188×	`fma-neg_binary64`

Counts

241 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	5266
1	807	4702
2	2560	4682
3	4533	4682
4	4986	4682
5	4935	4682

prune295.0ms (6.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	320	6	326

Error

Counts

326 → 6

Alt Table

Status	Error	Program
✓	1.9b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
✓	1.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 -1 (*.f64 (neg.f64 u) (/.f64 1 t1))))
	16.2b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	12.4b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 1 (.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))
✓	1.5b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))
	3.4b	(/.f64 v (*.f64 (-.f64 -1 (/.f64 u t1)) (+.f64 t1 u)))

Compiler

Compiled 7770 to 3402 computations (56.2% saved)

regimes591.0ms (12.2%)

Accuracy

Total 1.4b remaining (90.5%)

Threshold costs 0b (0%)

Counts

152 → 1

Compiler

Compiled 12298 to 7602 computations (38.2% saved)

simplify3.0ms (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	15	43
1	21	43
2	26	43
3	30	43
4	33	43
5	34	43
6	33	43

end88.0ms (1.8%)

Compiler: Compiled 162 to 102 computations (37% saved)

Details

analyze184.0ms (3.8%)

sample989.0ms (20.4%)

simplify76.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series101.0ms (2.1%)

rewrite54.0ms (1.1%)

simplify223.0ms (4.6%)

prune298.0ms (6.1%)

localize8.0ms (0.2%)

series88.0ms (1.8%)

rewrite37.0ms (0.8%)

simplify114.0ms (2.4%)

prune342.0ms (7.1%)

localize8.0ms (0.2%)

series102.0ms (2.1%)

rewrite43.0ms (0.9%)

simplify187.0ms (3.9%)

prune572.0ms (11.8%)

localize9.0ms (0.2%)

series107.0ms (2.2%)

rewrite35.0ms (0.7%)

simplify274.0ms (5.7%)

prune295.0ms (6.1%)

regimes591.0ms (12.2%)

simplify3.0ms (0.1%)

end88.0ms (1.8%)

Profiling