Details

analyze456.0ms (3.7%)

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
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample108.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 34 to 20 computations (41.2% saved)

simplify74.0ms (0.6%)

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%)

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
▶	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	21.0b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

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))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series91.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

68.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
16.0ms	(/.f64 v (+.f64 t1 u))
7.0ms	(-.f64 -1 (/.f64 u t1))

rewrite52.0ms (0.4%)

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:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
7.0ms	(-.f64 -1 (/.f64 u t1))
5.0ms	(/.f64 v (+.f64 t1 u))

simplify238.0ms (1.9%)

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

prune276.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	298	5	303
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	298	7	305

Error

Counts

305 → 7

Alt Table

Status	Error	Program
▶	0.7b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	21.0b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	4.3b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 8240 to 2936 computations (64.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 -1 (/.f64 u t1))
✓	0.0b	(/.f64 1 (+.f64 t1 u))
✓	0.2b	(*.f64 v (/.f64 1 (+.f64 t1 u)))
✓	0.6b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

series105.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

75.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
21.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
9.0ms	(/.f64 1 (+.f64 t1 u))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
31×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 119

Calls

3 calls:

14.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
8.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
6.0ms	(/.f64 1 (+.f64 t1 u))

simplify130.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-/r*_binary64`
449×	`associate-/r/_binary64`
415×	`associate-/l/_binary64`
366×	`fma-neg_binary64`
338×	`fma-def_binary64`

Counts

215 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3908
1	577	3653
2	2003	3521
3	4793	3521
4	5013	3521

prune253.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	284	7	291

Error

Counts

291 → 7

Alt Table

Status	Error	Program
✓	0.7b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	21.0b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	4.3b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 7160 to 3186 computations (55.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))
	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	19.9b	(cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

series2.6s (21.1%)

Counts

3 → 108

Calls

3 calls:

1.5s

(*.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

972.0ms

(cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

107.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

rewrite572.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

1539×	`times-frac_binary64`
1254×	`*-un-lft-identity_binary64`
1149×	`add-sqr-sqrt_binary64`
879×	`cbrt-prod_binary64`
486×	`add-cube-cbrt_binary64`

Counts

3 → 757

Calls

3 calls:

174.0ms

(*.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

74.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

14.0ms

(cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

simplify938.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

560×	`fma-def_binary64`
377×	`*-commutative_binary64`
287×	`times-frac_binary64`
274×	`associate-/l*_binary64`
254×	`associate-/l/_binary64`

Counts

865 → 871

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1149	47440
1	2543	46775
2	4838	46767
3	5181	46767

prune2.5s (20.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1732	0	1732
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1732	7	1739

Error

Counts

1739 → 7

Alt Table

Status	Error	Program
✓	0.7b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (/.f64 (cbrt.f64 v) (cbrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	21.0b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	4.3b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 98750 to 40986 computations (58.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	0.4b	(/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u))))
✓	9.6b	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

series1.3s (10.7%)

Counts

4 → 144

Calls

4 calls:

542.0ms	(*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u))))
363.0ms	(/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
313.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))
87.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))

rewrite174.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

533×	`times-frac_binary64`
460×	`add-sqr-sqrt_binary64`
425×	`*-un-lft-identity_binary64`
350×	`cbrt-prod_binary64`
213×	`add-cube-cbrt_binary64`

Counts

4 → 464

Calls

4 calls:

46.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
21.0ms	(*.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u))))
12.0ms	(/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
3.0ms	(cbrt.f64 (/.f64 v (+.f64 t1 u)))

simplify362.0ms (3%)

Algorithm

1×	egg-herbie

Rules

508×	`associate-/l*_binary64`
277×	`*-commutative_binary64`
277×	`fma-def_binary64`
251×	`times-frac_binary64`
197×	`associate-/l/_binary64`

Counts

608 → 653

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	888	22736
1	2346	21952
2	4974	21952

prune643.0ms (5.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	818	1	819
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	819	7	826

Error

Counts

826 → 7

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	21.0b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	0.7b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	4.3b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (cbrt.f64 (/.f64 v (+.f64 t1 u)))) (/.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))) (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 35153 to 12115 computations (65.5% saved)

regimes554.0ms (4.5%)

Accuracy

Total 1.2b remaining (89.9%)

Threshold costs 0b (0%)

Counts

119 → 1

Compiler

Compiled 11518 to 6882 computations (40.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end0.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample711.0ms (5.8%)

Algorithm

1×

intervals

Results

338.0ms	8000×	body	128	valid
18.0ms	279×	body	128	invalid

Compiler

Compiled 194 to 106 computations (45.4% saved)

Details

analyze456.0ms (3.7%)

sample108.0ms (0.9%)

simplify74.0ms (0.6%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series91.0ms (0.7%)

rewrite52.0ms (0.4%)

simplify238.0ms (1.9%)

prune276.0ms (2.3%)

localize9.0ms (0.1%)

series105.0ms (0.9%)

rewrite35.0ms (0.3%)

simplify130.0ms (1.1%)

prune253.0ms (2.1%)

localize10.0ms (0.1%)

series2.6s (21.1%)

rewrite572.0ms (4.7%)

simplify938.0ms (7.7%)

prune2.5s (20.5%)

localize12.0ms (0.1%)

series1.3s (10.7%)

rewrite174.0ms (1.4%)

simplify362.0ms (3%)

prune643.0ms (5.3%)

regimes554.0ms (4.5%)

simplify5.0ms (0%)

end0.0ms (0%)

sample711.0ms (5.8%)

Profiling