Details

analyze432.0ms (9.4%)

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%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.3s (28.5%)

Symmetry

(sort d2 d3)

Results

1.1s	7775×	body	128	valid
72.0ms	663×	body	128	invalid
52.0ms	199×	body	512	valid
51.0ms	161×	body	1024	valid
21.0ms	121×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	10

prune3.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 41 to 27 computations (34.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

series7.0ms (0.2%)

Counts

1 → 28

Calls

1 calls:

7.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

7.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
943×	`distribute-lft-in_binary64`
503×	`fma-neg_binary64`
394×	`associate-l_binary64`
294×	`associate-r_binary64`

Counts

54 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	601
1	162	559
2	683	559
3	2795	559
4	3172	559
5	4459	559
6	4975	559

prune37.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Error

0.0b

Counts

49 → 4

Alt Table

Status	Error	Program
▶	22.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
	36.6b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	28.6b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 759 to 417 computations (45.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
✓	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.3b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

series97.0ms (2.1%)

Counts

3 → 60

Calls

3 calls:

52.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
35.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))
10.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
16×	`associate-r_binary64`
16×	`sqrt-div_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 81

Calls

3 calls:

13.0ms	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
13.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
4.0ms	(sqrt.f64 (+.f64 3 (+.f64 d2 d3)))

simplify157.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
436×	`fma-neg_binary64`
421×	`*-commutative_binary64`
307×	`cancel-sign-sub-inv_binary64`
244×	`associate-l_binary64`

Counts

141 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	195	2457
1	510	2313
2	1664	2269
3	3116	2260
4	4816	2258
5	4998	2258
6	4950	2258

prune131.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	168	4	172

Error

Counts

172 → 4

Alt Table

Status	Error	Program
✓	22.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
▶	22.8b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	28.6b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 4477 to 2751 computations (38.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.2b	(cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.3b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))))
✓	0.4b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))))

series121.0ms (2.6%)

Counts

3 → 84

Calls

3 calls:

72.0ms

(cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

38.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))))

10.0ms

(*.f64 (*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))))

rewrite179.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

230×	`sqrt-div_binary64`
176×	`cbrt-div_binary64`
140×	`frac-times_binary64`
115×	`flip-+_binary64`
115×	`flip3-+_binary64`

Counts

3 → 208

Calls

3 calls:

52.0ms

(*.f64 (*.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))))

17.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))))

4.0ms

(cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))

simplify270.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

771×	`associate-l_binary64`
456×	`fma-def_binary64`
295×	`*-commutative_binary64`
172×	`times-frac_binary64`
168×	`associate--l+_binary64`

Counts

292 → 364

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	706	14600
1	1851	14009
2	5078	14009

prune764.0ms (16.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	558	0	558
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	558	4	562

Error

Counts

562 → 4

Alt Table

Status	Error	Program
✓	22.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	22.8b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	28.6b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 33526 to 22096 computations (34.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))
✓	0.0b	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
✓	9.6b	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
✓	17.3b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

series122.0ms (2.7%)

Counts

4 → 120

Calls

4 calls:

69.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
36.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
10.0ms	(-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))
6.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 131

Calls

4 calls:

9.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
7.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
7.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
3.0ms	(-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))

simplify136.0ms (3%)

Algorithm

1×	egg-herbie

Rules

275×	`fma-neg_binary64`
239×	`associate-r_binary64`
237×	`associate-/l*_binary64`
217×	`associate-l_binary64`
196×	`times-frac_binary64`

Counts

251 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	5968
1	987	5340
2	4202	5208
3	4985	5208

prune184.0ms (4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	261	4	265

Error

Counts

265 → 4

Alt Table

Status	Error	Program
✓	22.7b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	22.8b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3)))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	28.6b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 7321 to 3435 computations (53.1% saved)

regimes371.0ms (8.1%)

Accuracy

Total 0.0b remaining (81.2%)

Threshold costs 0.0b (81.2%)

Counts

80 → 1

Compiler

Compiled 7376 to 4852 computations (34.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end76.0ms (1.7%)

Remove: (sort d2 d3)
Compiler: Compiled 123 to 81 computations (34.1% saved)

Details

analyze432.0ms (9.4%)

sample1.3s (28.5%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series7.0ms (0.2%)

rewrite9.0ms (0.2%)

simplify69.0ms (1.5%)

prune37.0ms (0.8%)

localize6.0ms (0.1%)

series97.0ms (2.1%)

rewrite35.0ms (0.8%)

simplify157.0ms (3.4%)

prune131.0ms (2.9%)

localize10.0ms (0.2%)

series121.0ms (2.6%)

rewrite179.0ms (3.9%)

simplify270.0ms (5.9%)

prune764.0ms (16.7%)

localize8.0ms (0.2%)

series122.0ms (2.7%)

rewrite36.0ms (0.8%)

simplify136.0ms (3%)

prune184.0ms (4%)

regimes371.0ms (8.1%)

simplify2.0ms (0%)

end76.0ms (1.7%)

Profiling