Details

analyze306.0ms (13.7%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	56.2%	3.3%	9
46.8%	46%	7.2%	10
58.5%	32.8%	8.7%	11
60.8%	27.9%	11.3%	12
63.8%	22.4%	13.8%	13
69.1%	16.5%	14.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample35.0ms (1.6%)

Algorithm

1×

intervals

Symmetry

(sort d2 d3)

Results

9.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`distribute-lft-out_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	13	7
2	18	7
3	18	7

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d2 d3))

Compiler

Compiled 31 to 18 computations (41.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 d1 (+.f64 d2 d3))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

(*.f64 d1 (+.f64 d2 d3))

simplify91.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

935×	`distribute-rgt-in_binary64`
925×	`distribute-lft-in_binary64`
590×	`fma-def_binary64`
549×	`fma-neg_binary64`
280×	`associate-l_binary64`

Counts

49 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	416
1	133	386
2	419	386
3	1050	386
4	3209	386
5	3409	386
6	4244	386
7	4814	386
8	4885	386

prune22.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	4	43

Error

0.0b

Counts

43 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
▶	1.3b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d2 d3)))
	37.9b	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (+.f64 (.f64 d2 d2) (-.f64 (.f64 d3 d3) (.f64 d2 d3))))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 d1 (+.f64 d2 d3))) (cbrt.f64 (.f64 d1 (+.f64 d2 d3)))) (cbrt.f64 (*.f64 d1 (+.f64 d2 d3))))

Compiler

Compiled 549 to 181 computations (67% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 d1) (+.f64 d2 d3))
✓	0.3b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d2 d3)))
✓	0.5b	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
✓	0.6b	(cbrt.f64 d1)

series225.0ms (10.1%)

Counts

4 → 96

Calls

4 calls:

134.0ms	(*.f64 (cbrt.f64 d1) (+.f64 d2 d3))
37.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
35.0ms	(cbrt.f64 d1)
19.0ms	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d2 d3)))

rewrite25.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64`

Counts

4 → 114

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 d2 d3)))
5.0ms	(*.f64 (cbrt.f64 d1) (+.f64 d2 d3))
4.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
1.0ms	(cbrt.f64 d1)

simplify125.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

646×	`distribute-rgt-in_binary64`
633×	`distribute-lft-in_binary64`
500×	`*-commutative_binary64`
329×	`unswap-sqr_binary64`
294×	`associate-+l+_binary64`

Counts

210 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1988
1	319	1771
2	1238	1718
3	3321	1703
4	4872	1691
5	5000	1691
6	4922	1691

prune73.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	202	3	205

Error

0.0b

Counts

205 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
▶	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1))) (+.f64 d2 d3)))
	37.9b	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (+.f64 (.f64 d2 d2) (-.f64 (.f64 d3 d3) (.f64 d2 d3))))

Compiler

Compiled 3406 to 794 computations (76.7% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1))) (+.f64 d2 d3)))
	0.5b	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
✓	0.6b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1)))
	0.6b	(cbrt.f64 d1)

series50.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

30.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1)))

20.0ms

(*.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1))) (+.f64 d2 d3)))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`cbrt-unprod_binary64`
8×	`prod-exp_binary64`
8×	`pow-prod-down_binary64`

Counts

2 → 42

Calls

2 calls:

9.0ms

(*.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1))) (+.f64 d2 d3)))

5.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1)))

simplify49.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-def_binary64`
543×	`distribute-rgt-in_binary64`
542×	`distribute-lft-in_binary64`
481×	`unswap-sqr_binary64`
349×	`*-commutative_binary64`

Counts

90 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	706
1	212	623
2	800	621
3	2705	621
4	4971	621

prune88.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	278	3	281

Error

0.0b

Counts

281 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1))) (+.f64 d2 d3)))
▶	37.9b	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (+.f64 (.f64 d2 d2) (-.f64 (.f64 d3 d3) (.f64 d2 d3))))

Compiler

Compiled 6468 to 1361 computations (79% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 (.f64 d3 d3) (.f64 d2 d3))
✓	2.5b	(+.f64 (pow.f64 d2 3) (pow.f64 d3 3))
✓	4.5b	(*.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3)))
✓	33.8b	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (+.f64 (.f64 d2 d2) (-.f64 (.f64 d3 d3) (.f64 d2 d3))))

series164.0ms (7.4%)

Counts

4 → 90

Calls

4 calls:

117.0ms	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (+.f64 (.f64 d2 d2) (-.f64 (.f64 d3 d3) (.f64 d2 d3))))
30.0ms	(*.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3)))
12.0ms	(+.f64 (pow.f64 d2 3) (pow.f64 d3 3))
5.0ms	(-.f64 (.f64 d3 d3) (.f64 d2 d3))

rewrite42.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`fma-def_binary64`
11×	`cube-prod_binary64`
11×	`unpow-prod-down_binary64`

Counts

4 → 105

Calls

4 calls:

14.0ms	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (+.f64 (.f64 d2 d2) (-.f64 (.f64 d3 d3) (.f64 d2 d3))))
12.0ms	(*.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3)))
8.0ms	(+.f64 (pow.f64 d2 3) (pow.f64 d3 3))
3.0ms	(-.f64 (.f64 d3 d3) (.f64 d2 d3))

simplify71.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
700×	`distribute-rgt-in_binary64`
506×	`times-frac_binary64`
213×	`cancel-sign-sub-inv_binary64`
177×	`associate-l_binary64`

Counts

195 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	2841
1	423	2568
2	1907	2562
3	5393	2562

prune76.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (cbrt.f64 d1))) (+.f64 d2 d3)))
	37.9b	(/.f64 (.f64 d1 (+.f64 (pow.f64 d2 3) (pow.f64 d3 3))) (fma.f64 d3 (-.f64 d3 d2) (.f64 d2 d2)))

Compiler

Compiled 4390 to 1750 computations (60.1% saved)

regimes182.0ms (8.2%)

Accuracy

Total 0.0b remaining (31.2%)

Threshold costs 0.0b (31.2%)

Counts

49 → 1

Compiler

Compiled 3392 to 1962 computations (42.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	8	7

end6.0ms (0.3%)

Remove: (sort d2 d3)
Compiler: Compiled 24 to 15 computations (37.5% saved)

sample528.0ms (23.7%)

Algorithm

1×

intervals

Results

223.0ms	8000×	body	128	valid
19.0ms	673×	body	128	invalid

Compiler

Compiled 73 to 43 computations (41.1% saved)

Details

analyze306.0ms (13.7%)

sample35.0ms (1.6%)

simplify9.0ms (0.4%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify91.0ms (4.1%)

prune22.0ms (1%)

localize7.0ms (0.3%)

series225.0ms (10.1%)

rewrite25.0ms (1.1%)

simplify125.0ms (5.6%)

prune73.0ms (3.3%)

localize8.0ms (0.4%)

series50.0ms (2.2%)

rewrite17.0ms (0.7%)

simplify49.0ms (2.2%)

prune88.0ms (4%)

localize11.0ms (0.5%)

series164.0ms (7.4%)

rewrite42.0ms (1.9%)

simplify71.0ms (3.2%)

prune76.0ms (3.4%)

regimes182.0ms (8.2%)

simplify2.0ms (0.1%)

end6.0ms (0.3%)

sample528.0ms (23.7%)

Profiling